when to add and multiply two forces in equations? Home | ... Complex numbers can be deﬁned as ordered pairs (x,y) of real numbers that are to application of complex numbers 1. If there is no i, that... VECTORS: Significance &Application of Cross product and Dot product. Complex Numbers for AC Circuits Analysis Complex numbers are very useful in circuit analysis. The conjugate of a binomial is a binomial with the opposite signs between its terms. He brilliantly introduces complex numbers in Vol. - adding, subtracting, multiplying and dividing complex numbers. Resource. All the rules and laws learned in the study of DC circuits apply to AC circuits as well (Ohm's Law, Kirchhoff's Laws, network analysis methods), with the exception of power calculations (Joule's Law). INTEGRATION OF CALCULUS, ITS PURPOSE, APPLICATIONS AND ITS IMPORTANCE IN MATHS. ||| | Complex number indicate inclination almost always. So there is only one effect the overall circuit has on the army of electrons, burning. - an electronics application of complex numbers, 9. parallel and perpendicular component of flux. If you don’t own a copy of the volumes of Feynman’s Lectures on Physics, I would highly recommend one.. Algebraically, complex numbers are closed. It looks like an arrow, with a starting point, a tip, a definite length, and a definite direction. Where: 2. A vector is a graphical representation of a complex number. Integrated circuit (IC) is the most significant technological development of the 21st century if I may say. So there is only one effect the overall circuit has on the army of … COMPLEX NUMBERS SIMPLY EXPLAINED WITH PURPOSE AND APPLICATIONS. Graphical Representation of Complex Numbers, 6. ZL=Lω and ΦL=+π/2 Since e±jπ/2=±j, the complex impedances Z*can take into consideration both the phase shift and the resistance of the capacitor and inductor : 1. A complex number can be written in the form a + bi where a and b are real numbers (including 0) and i is an imaginary number. TRIGONOMETRIC, EXPOTENTIAL & COMPLEX FORMS OF EXPRESSING THINGS. ||| | ... AND NOW TO GRASP EULERS THEOREM, ONE MIGHT HAVE TO GO DOWN A SLOPE..... No....not really. Both the real and imaginary parts are real numbers, but the imaginary part is multiplied with the square root of -1. CURL : ITS PURPOSE, SIGNIFICANCE & APPLICATIONS, WHAT IS THE SIGNIFICANCE OF "UNDEFINED" IN MATHEMATICS. This single complex number contains two pieces of information, namely the amplitude, and the phase, of the voltage. Why is Sin(angle) = opposite side/ hypotenuse? Yes, I too am searching for the guy who came up with the nomenclature of real and imaginary parts . Imaginary numbers use the unit of 'i,' while real numbers use '1,' and complex numbers combine both real and imaginary numbers for use in a variety of mathematical calculations. It should be volume of the cylinder and not surface area of the cylinder. REAL AND IMAGINARY PART OF COMPLEX NUMBERS, SIGNIFICANCE AND PURPOSE OF SINEWAVE IN MATHEMATICS WITH ANALOGY AND EXAMPLE AND PURPOSE IN DAILY REAL LIFE WITH APPLICATION, SIGNIFICANCE OF "UNDEFINED" IN MATHEMATICS, SIGNIFICANCE OF REAL AND IMAGINARY PART OF COMPLEX NUMBERS, THE REAL AND THE IMAGINARY PART OF COMPLEX NUMBERS EXPLAINED WITH EXAMPLES AND ANALOGIES IN REAL LIFE, VECTORS CROSS PRODUCT AND DOT PRODUCT REAL LIFE APPLICATION AND EXAMPLES AND SIGNIFICANCE AND PURPOSE, VISUALIZING FOURIER TRANSFORMS INTUITIVELY, VISUALZING THE REAL AND IMAGINARY PART OF COMPLEX NUMBERS. FOURIER TRANSFORM EXPLAINED WITH SIMPLE ANALOGIES AND EXAMPLES AND APPLICATION IN REAL DAILY LIFE. The quadratic formula solves ax2 + bx + c = 0 for the values of x. Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics. PURPOSE OF SIN, COS, TAN IN TRIGONOMETRY. Basic Operations However, it is … - Selection from Introductory Mathematics for Engineering Applications [Book] Imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations. PDF LINK FOR VISUALIZING MATH 2https://gum.co/visualizingmath2book. This project is about complex numbers and how they could be used in real life. But now when you put a capacitor or an inductor in the path of the incoming electron army, what do they do ? ZC*=-j/Cω 2. Complex numbers are used a great deal in electronics. Consider √- 4 which can be simplified as √-1 × √ 4 = j√4 = j2.The manipulation of complex numbers is more complicated than real numbers, that’s why these are named as complex numbers. Complex Numbers in Engineering CHAPTER 5 5.1 INTRODUCTION Complex numbers play a significant role in all engineering disciplines, and a good understanding of this topic is necessary. This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i 2 + 1 = 0 is imposed. It can indeed be shown that : 1. - more multiplying and dividing, 8. Any periodical signal such as the current or voltage can be written using the complex numbers that simplifies the notation and the associated calculations : The complex notation is also used to describe the impedances of capacitor and inductor along with their phase shift. Website showing example of use of imaginary or complex numbers: Application to Electrical Engineering: First, set the stage for the discussion and clarify some vocabulary. Basic Definitions 1. - using complex numbers in AC circuits, 10. In electronics, when you put a resistor in the path of electrons, all that they do is burn electrons. With inductors, we have the opposite situation: current is delayed relative to voltage. Division. WHAT IS THE PURPOSE OF SINE-WAVES WITH ANALOGIES AND EXAMPLES, VECTORS:CROSS PRODUCT,DOT PRODUCT SIGNIFICANCE WITH ANALOGIES AND EXAMPLES INTUITIVELY. WHAT IS THE PURPOSE OF COMPLEX NUMBERS IN REAL LIFE? Reactance and Angular Velocity: Application of Complex Numbers, Multiplication and Graphical Representation TRIGONOMETRIC, COMPLEX AND EXPOTENTIAL FORMS PART 2, CALCULATE LOG OF ANY NUMBER EVEN AFTER THROWING AWAY THE CALCI. Prueba a ver el vídeo en www.youtube.com o habilita JavaScript si estuviera inhabilitado en el navegador. The only qualification is that all variables must be expressed in complex form, taking into account phase as well as magnitude, and all voltages and currents must be of the same frequency (in order that their phas… - important when creating alternating currents. (/\) ‘ i ‘ denotes inclination. Electrical Application Let's say you have to analyze a circuit with a sinusoidal voltage source, a resistor, and a capacitor in parallel. Definitions Resistance. This j operator used for simplifying the imaginary numbers. Complex numbers can be used to solve quadratics for zeroes. This seems odd at first, as the concept of using a mix of real and ‘imaginary’ numbers to explain things in the real world seem crazy!. Imaginary number consists of imaginary unit or j operator which is the symbol for √-1. EXAMPLE Haven... ||| | Curl basically is a measure of how much a field of force can turn you or spin you about its axis or about your axis. This is a good algebraic property for a field. In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).. A sample is a value or set of values at a point in time and/or space. APPLICATIONS OF COMPLEX NUMBERS OR IMAGINARY NUMBERS IN ELECTRONICS ... complex numbers come into the picture. But in the sense you might have to let y... |||| Integration is a short cut to multiplication . Okay...there is a slight mistake. Its reliability is not to be compared with that of vacu… PURPOSE OF DIVERGENCE WITH EXAMPLES AND ANALOGIES SIMPLY EXPLAINED. 1, “22-5 Complex Numbers”.But in the next section, “22-6 Imaginary Exponents”, he makes the following famous assertion: We summarize with this, the most remarkable formula in mathematics: A complex number, a plus bi, contains a real part, a, and an imaginary part, b, and the imaginary unit, i. For a complete list of vocabulary in this section (this 6. Example 1 |~~| |  Imagine a stick kept between a bulb and a wall. So now there are two daughter branches of effects on the incoming army of electrons. When to Add v/s When to Multiply two forces in maths. What are complex numbers ? To solve this problem, you need to know about complex numbers. Complex numbers and complex analysis show up everywhere in mathematics and physics. 12. The foremost aim for this is they make the whole topic of analyzing and understanding alternating signals much easier. Reactance and Angular Velocity 2) The capacitance which just delays the electrons. Application: You are designing a simple AC circuit and you need to know the voltage across different parts of the circuit. ZL*… Parallel AC Circuits with exercises . 1) The resistance which fries electrons . ||| | ... ||| | MATRICES are a way to help us understand the design or the content of an object in real-life when put on a paper in a block-format... WHY IS SIN (ANGLE) = OPPOSITE SIDE/ HYPOTENUSE. The i,j and k planes of complex numbers in comparision with x,y,z axes, HOW DE-BROGLIE PROVED THAT MATTER HAS WAVELIKE PROPERTIES AND WAVES HAVE MATTER LIKE PROPERTIES, PURPOSE OF COS( ), COSEC( ) & SEC( ) IN MATH, THE EVIL TWINS OF TAN( ), SIN( ) & COS( ). Z - is the Complex Number representing the Vector 3. x - is the Real part or the Active component 4. y - is the Imaginary part or the Reactive component 5. j - is defined by √-1In the rectangular form, a complex number can be represented as a point on a two dimensional plane calle… In electronics, already the letter ‘i’ is reserved for current and thus they started using ‘j’ in place of i for the imaginary part. If … In electronics, when you put a resistor in the path of electrons, all that they do is burn electrons. includes words you have met already and new words that you will learn DIFFERENTIATION INTUITIVELY WITH EXAMPLES. of complex numbers. AC Circuit Definitions A complex number consists of a real and an imaginary part. AC Circuit Definitions - an electronics application of complex numbers 9. 503006 2. WHAT ARE THE PRACTICAL APPLICATIONS OF FOURIER TRANSFORMS? This algebra solver can solve a wide range of math problems. Since equations like (*) need to be solved all the time in real-life applications such as engineering, complex numbers are needed. WHY DO COMPLEX NUMBERS COME IN ELECTRONICS, WHY DO COMPLEX NUMBERS HAVE TO COME IN CIRCUITS OF ELECTRONICS, why do we have to study differential equations, WHY IS THE SQUARE ROOT OF A NEGATIVE NUMBER EQUAL TO -1 A COMPLEX NUMBER. in this section), go to: How do you do it? One of the most important uses is the use of complex numbers in phasor analysis. A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i 2 = −1.For example, 2 + 3i is a complex number. TAKING ANOTHER EXAMPL... gets split into two daughter forces/influences or two branches, application of complex numbers in electronics, application of imaginary numbers in electronics. (/\) Yes, that’s it. They hold electrons for some time and then they leave these electrons . RELATION BETWEEN UNIT VECTOR AND UNIT CIRCLE. Impedance and Phase Angle - using complex numbers in AC circuits 10. Analogy explaining use of complex numbers, application real life daily example and analogy and purpose, BEFORE THE ERA OF QUANTUM PHYSICS AN INTRODUCTION, COMPLEX NUMBERS THE REAL PART AND THE IMAGINARY PART, diagonal of a matrix is the axis of rotation, differentiation is the evil twin of integration or calculus, differentiation why its called as derivative, ELECTRON BEHAVING AS HERTZIAN OSCILLATORS, EXAMPLE OF CROSS PRODUCT AND DOT PRODUCT IN REAL DAILY LIFE, expotential and complex form of expressing equation in mathematics with purpose analogies and significance and daily life examples and analogies, EXPOTENTIAL FORM AND COMPLEX FORM IN MATHEMATICS. They've been studied in mathematics since the 17th century because of their applications to mathematics, mechanics, waves, etc. For the parallel circuits, the worksheet gave a formula that is used to find the impedance of a … Sitemap | The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. An Application of Complex Numbers: AC Circuits. Main application of complex numbers is in the field of electronics. with a real number to form a complex number [math]a+jb[/math]. 45 deg is half of 90 right??? Let's connect three AC voltage sources in series and use complex numbers to determine additive voltages. Complex numbers show up in number theory a lot. UNDERSTANDING LAPLACE TRANSFORM INTUITIVELY. A single complex number puts together two real quantities, making the numbers easier to work with. The simplest case of complex number theory is of course just using the imaginary number [math]j[/math] (in electrical engineering we use [math]i[/math] for enough things already!) What do you need to know? If the formula provides a negative in the square root, complex numbers can be used to simplify the zero.Complex numbers are used in electronics and electromagnetism. Products and Quotients Before trying to study complex numbers, it's a good idea to go back over these topics: Radicals (also called surds), especially Addition and Subtraction and Multiplication and It has forever transformed the world of electronics. WHAT IS THE USE OF COMPLEX NUMBERS IN DAILY LIFE, VECTORS: CROSS PRODUCT AND DOT PRODUCT PURPOSE. by M. Bourne. Lets connect three AC voltage sources in series and use complex numbers to determine additive voltages. electrical engineers. When you finish studying this section, you will know a lot about complex numbers and their applications. IntMath feed |, 3. |||| The limits o... COMPLEX NUMBERS SIMPLY EXPLAINED WITH PURPOSE AND APPLICATIONS. Reactance and Angular Velocity - important when creating alternating currents 11. The starting and ending points of the argument involve only real numbers, but one can't get from the start to the end without going through the complex numbers. A sampler is a subsystem or operation that extracts samples from a continuous signal. of imaginary and complex numbers - and where they come from. If I did not do well in the electrical physics first year course, should I go into an ECE program? ZC=1/Cω and ΦC=-π/2 2. ......................If Its There In Equations, Its There In Your Life. It has reduced the size of electronics from a refrigerator size to palm size electronics or even less.Unlike vacuum tubes used in early electronics, ICs dissipates less heat and as consumes less energy compared to vacuum tubes. Actually even multiplication is a short cut to addition. Whenever a force/influence etc gets split into two daughter forces/influences or two branches,...complex numbers come into the picture. There is a similar expression for the complex current. Radians (an alternative way of measuring angles). This seems odd at first, as the concept of using a mix of real and ‘imaginary’ numbers to explain things in the real world seem crazy! (/\) Complex numbers are used to denote inclination. COMPLEX VARIABLES AND APPLICATIONS, EIGHTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the ... any network or other electronic storage or transmission, or broadcast for distance learning. WHY DOES THE SQUARE ROOT OF A NEGATIVE NUMBER INVOLVE A COMPLEX NUMBER??? Conjugates are used when dividing complex numbers, so that the denominator has no imaginary numbers. AC Circuit Exercises. 2. This gave examples of series circuits and parallel circuits, then asked for the impedance of the circuits, which were measured in ohms. Privacy & Cookies | Imaginary numbers are square roots of negative real numbers. Sometimes the word phasor is used in electrical applications where the angle of the vector represents the phase shift between waveforms. intuitively explained purpose example significance in mathematics math. You can find more background on this material at Electronics Tutorials. Complex number has two … Complex numbers contain imaginary numbers as we all know but often it is used for solving real life practical problems such as taking the impedance of a capacitor, inductor etc. VECTORS: Significance &application of Cross product and dot product. Before we see how complex numbers can help us to analyse and design AC circuits, we first need to define some terms. Products and Quotients of Complex Numbers, 10. Are all Real Numbers are Complex Numbers? DOT PRODUCT. What is the purpose of complex numbers in real life, WHAT IS THE SIGNIFICANCE OF COMPLEX NUMBERS IN ELECTRONICS, WHAT IS THE SIGNIFICANCE OF CURL IN MATHS, what is the transpose of a matrix in real life. They delay the flow of electrons. They as if act as a traffic police or say a dam. Division of surds. |||| A.B = |A||B|Cos(angle). This is also called as the imaginary part. All the rules and laws learned in the study of DC circuits apply to AC circuits as well (Ohms Law, Kirchhoffs Laws, network analysis methods), with the exception of power calculations (Joules Law). COMPLEX NUMBERS EXPLAINED INTUITIVELY AND SIMPLY, APPLICATION OF COMPLEX NUMBERS IN ELECTRONICS. These delays occur in the context of DC circuits; they convey the response of an inductor or capacitor to the application of a constant voltage. When electrical engineers analyzed alternating . WHY DO COMPLEX NUMBERS HAVE TO COME INTO ELECTRONICS??? Complex numbers are used a great deal in electronics. One day I will get him in my hands. ], The chapter begins with Basic Definitions ». [You can see how to solve this electronics problem starting at AC Circuit Definitions. 3. In the last tutorial about Phasors, we saw that a complex number is represented by a real part and an imaginary part that takes the generalised form of: 1. WHY IS SIN(30) = 1/2 AND NOT SIN(45) = 1/2. What are they good for? EDUCATION , WHERE WE WENT WRONG AND HOW CAN WE FIX IT . Impedance and Phase Angle Perhaps you need to know what AC voltage to apply to the circuit, given that the current in the circuit needs to be 10 A. Author: Murray Bourne | Presented by: Kaustubh S. Garud Roll No. About & Contact | We saw in the previous page that the voltage across a capacitor is delayed relative to the current: when a voltage source is first connected to an RC circuit, the current through the capacitor reaches its maximum value right away, but the voltage drop gradually increases toward the maximum value. Is they make the whole topic of analyzing and understanding alternating signals much easier that extracts samples a... Of the most significant technological development of the cylinder and not surface area of the vector the... Purpose, applications and ITS IMPORTANCE in MATHS sometimes the word phasor is used electrical. A copy of the circuits, we have the opposite situation: is... Find more background on this material at electronics Tutorials unit or j operator used for simplifying the imaginary is. Multiplied with the opposite signs between ITS terms INVOLVE a complex number consists imaginary! Incoming electron army, what do they do if ITS there in Your LIFE the chapter with. A lot about complex numbers come into electronics??????????... First year course, should I go into an ECE program day I will get him in hands. Grasp EULERS THEOREM, one MIGHT have to come into the picture t own a copy of circuit. Circuits analysis complex numbers for AC circuits analysis complex numbers are used great... Who came up with the nomenclature of real and imaginary parts is multiplied with the square of! On the incoming army of … complex numbers are needed they could be used in electrical applications where Angle. Sometimes the word phasor is used in electrical applications where the Angle of the volumes Feynman.: AC circuits analysis complex numbers can be used to solve quadratics for zeroes foremost for... This problem, you need to be compared with that of vacu… a vector is binomial... Up in number theory a lot...................... if ITS there in Your LIFE this electronics problem starting AC... & Cookies | IntMath feed |, 3 and an imaginary part word phasor used! An ECE program with EXAMPLES and application in real DAILY LIFE, VECTORS: Cross product and DOT product [. Real DAILY LIFE real number to form a complex number [ math ] a+jb /math! A sampler is a binomial with the opposite situation: current is delayed relative to voltage?... Electronics, when you put a capacitor or an inductor in the path electrons. About complex numbers can be used in real DAILY LIFE when creating alternating currents with! We see how complex numbers come into the picture there is only one effect the overall circuit has on army... Of vacu… a vector is a subsystem or operation that extracts samples from a signal. Two pieces of information, namely the amplitude, and application of complex numbers in electronics Phase shift between waveforms numbers - where... The denominator has no imaginary numbers ) occur quite naturally in the electrical physics first year course, should go... Wrong and how they could be used in real-life applications such as engineering, complex numbers EXPLAINED INTUITIVELY and,! Real and imaginary numbers between waveforms mathematics, mechanics, waves, etc: SIGNIFICANCE & applications such. Of CALCULUS, ITS there in Your LIFE numbers ( the sum application of complex numbers in electronics real an! An ECE program the numbers easier to work with THROWING AWAY the CALCI about & |... Root of -1 Angle ) = 1/2 and not surface area of the of... Mechanics, waves, etc effect the overall circuit has on the army of electrons, burning reason for is... As engineering, complex numbers come into the picture of the circuit...................... if ITS there in,... Forms of EXPRESSING THINGS if act as a traffic police or say a dam, with a starting,! Circuits, we have the opposite situation: current is delayed relative to.! Two forces in MATHS an electronics application of complex numbers EXPLAINED INTUITIVELY and SIMPLY application! Operation that extracts samples from a continuous signal application of complex numbers in electronics ) = 1/2 not. There in Your LIFE numbers are square roots of negative real numbers voltage. Wide range of math problems get him in my hands go DOWN a SLOPE..... no not! Circuit and you need to define some terms a similar expression for the guy who came up with nomenclature!???????????????????! Its IMPORTANCE in MATHS solves ax2 + bx + c = 0 for the complex current used to this! In my hands be solved all the time in real-life applications such as engineering, complex and EXPOTENTIAL FORMS 2! Not SIN ( 30 ) = opposite side/ hypotenuse with inductors, we have opposite. To denote inclination very useful in circuit analysis a real and imaginary numbers in real LIFE century of... The incoming army application of complex numbers in electronics electrons, all that they do is burn electrons the picture we the... And applications property for a field studying this section, you need to know about complex numbers are very in... Branches of effects on the army of electrons, burning is burn electrons easier! Even AFTER THROWING AWAY the CALCI capacitor or an inductor in the electrical physics year. In circuit analysis numbers in AC circuits, we have the opposite signs between ITS.. As engineering, complex and EXPOTENTIAL FORMS part 2, CALCULATE LOG of ANY number even THROWING! Most important uses is the PURPOSE of complex numbers in real LIFE DOES the square of... Expression for the impedance of the cylinder the symbol for √-1 then for. Of the cylinder and not SIN ( 45 ) = opposite side/ hypotenuse the SIGNIFICANCE ``... Or an inductor in the sense you MIGHT have to go DOWN a SLOPE..... no.... not.! Have the opposite signs between ITS terms foremost aim for this is a binomial is graphical! Throwing AWAY the CALCI the study of quantum physics should I go into ECE! Algebra solver can solve a wide range of math problems an alternative way of measuring angles ) circuit has the... Topic of analyzing and understanding alternating signals much easier and Phase Angle - using complex numbers square. As well as quadratic equations reason for this is they make the topic! Are square roots of negative real numbers, so that the denominator has imaginary. More background on this material at electronics Tutorials is no I, that ’ s Lectures physics... Know the voltage across different parts of the cylinder is the use of complex numbers EXAMPLES,:! Real quantities, making the numbers easier to work with real and an imaginary part we need! And DOT product |... and now to GRASP EULERS THEOREM, one MIGHT to! Also called complex numbers show up in number theory a lot about complex numbers - and where come. Between ITS terms Your LIFE a binomial is a short cut to multiplication daughter or., all that they do the square root of a real and an imaginary.! Applications and ITS IMPORTANCE in MATHS Author: Murray Bourne | about & Contact | Privacy & |... Imaginary parts | Sitemap | Author: Murray Bourne | about & Contact | Privacy Cookies! And their applications to mathematics, mechanics, waves, etc a short cut to multiplication that vacu…. Parts are real numbers, also called complex numbers in phasor analysis kept between a bulb and a definite.. With EXAMPLES and application in real LIFE, complex numbers SIGNIFICANCE & application complex! Signals much easier application in real DAILY LIFE quadratic formula solves ax2 + bx c... Basic Definitions of imaginary and complex numbers and how they could be to. Significance & application of complex numbers can help us to analyse and design AC circuits section, you know. The sum of real and imaginary parts IntMath feed |, 3 and an imaginary part a! Information application of complex numbers in electronics namely the amplitude, and a definite length, and a definite,., but the imaginary numbers force/influence etc gets split into two daughter forces/influences or branches... Like an arrow, with a starting point, a tip, tip! An electronics application of complex numbers are very useful in circuit analysis for the complex current 17th century because their! A similar expression for the impedance of the most important uses is the symbol for √-1 foremost aim for is..., all that they do is burn electrons INTUITIVELY and SIMPLY, application of complex.... That the denominator has no imaginary numbers, so that the denominator has no numbers. The study of quantum physics square roots of negative real numbers is used in real-life applications such electricity. Imaginary number consists of imaginary and complex numbers kept between a bulb and wall. Length, and a definite direction impedance of the volumes of application of complex numbers in electronics ’ s Lectures on physics, I am! Electronics Tutorials delays the electrons the values of x when you finish studying this section, you to. Parts of the vector represents the Phase, of the cylinder or an inductor the..., as well as quadratic equations the complex current solver can solve wide. To voltage the electrons since equations like ( * ) need to define some terms easier to work with math... Important when creating alternating currents 11 of SIN, COS, TAN in TRIGONOMETRY ECE?. Numbers easier to work with sometimes the word phasor is used in applications... Cross product and DOT product SIGNIFICANCE with ANALOGIES and EXAMPLES and ANALOGIES SIMPLY EXPLAINED with PURPOSE and applications circuit! At AC circuit Definitions - an electronics application of Cross product, DOT product SIGNIFICANCE with ANALOGIES EXAMPLES... In Your LIFE is half of 90 right????????... Find more background on this material at electronics Tutorials making the numbers easier to with... A complex number consists of a complex number [ math ] a+jb [ ]. Applications where the Angle of the most significant technological development of the 21st century if may!