# Use of complex numbers in electrical engineering. Application of complex number in engineering 2022-11-01

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Complex numbers are a mathematical concept that have found numerous applications in electrical engineering. They consist of a real part and an imaginary part, and can be represented in the form a + bi, where a is the real part and bi is the imaginary part. The imaginary unit, denoted by "i", is defined as the square root of -1.

One of the main uses of complex numbers in electrical engineering is in the analysis and design of electrical circuits. Complex numbers are particularly useful in this context because they allow engineers to represent both the magnitude and phase of a quantity, such as an electrical current or voltage.

For example, consider an electrical circuit that contains an inductor, which is a passive electrical component that stores energy in the form of a magnetic field. The current through an inductor is not in phase with the voltage across it, meaning that the phase angle between the current and voltage is not zero. By representing the current and voltage as complex numbers, it is possible to easily calculate the phase angle between them, which is important for understanding the behavior of the circuit.

Another important use of complex numbers in electrical engineering is in the analysis of alternating current (AC) systems. AC systems are commonly used to distribute electrical power over long distances, and the voltage and current in these systems oscillate at a specific frequency. By representing the voltage and current as complex numbers, it is possible to analyze the phase relationship between them, as well as the power being transmitted in the system.

Complex numbers are also used in electrical engineering to represent the impedance of electrical components, such as resistors, capacitors, and inductors. Impedance is a measure of the opposition to the flow of electrical current in a circuit, and it is complex-valued because it includes both resistance (a real quantity) and reactance (an imaginary quantity). By representing impedance as a complex number, it is possible to easily calculate the total impedance of a circuit, which is important for understanding the behavior of the circuit.

In summary, complex numbers are an essential tool in electrical engineering, with numerous applications in the analysis and design of electrical circuits, the analysis of AC systems, and the representation of impedance. Their ability to represent both magnitude and phase makes them a powerful tool for understanding and predicting the behavior of electrical systems.

## How complex variables used in electrical engineering

Complex numbers are commonly used in electrical engineering, as well as in physics. To represent these kinds of quantities, we need multidimensional representations. The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis. Applications of complex numbers in engineering Signal Analysis: Complex numbers are used in signal analysis and other fields to obtain a convenient description of signals that vary periodically. Several methods exist to do this; see methods of contour integration. Complex numbers have two components: real and imaginary.

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## Why are complex numbers important in electrical engineering

Oh, it's just the set theory version of a function. Although imaginary numbers are not commonly used in daily life, in engineering and physics they are in fact used to represent physical quantities such as impedance of RL, RC, or RLC circuit. What is the significance of complex numbers? This then produces a complex plane with four quadrants called an Argand Diagram as shown below. This approach is called phasor calculus. It is fuzzy, but somewhere along the line, mathematicians added the concept of non-integer or rational numbers, e. Complex numbers, triangles, circles, and sine waves are related.

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## Complex Numbers & Phasors in Polar and Rectangular Form

It's quite useful in circuit analysis - unfortunately, it's also quite limited, since it only applies to resistors. So it certainly doesn't hurt to dig a little deeper into the theory of complex numbers and complex functions. In short, they are critical to modern electrical engineering, a realization made over a century ago. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. Application in electronics engineering Information that expresses a single dimension, such as linear distance, is called a scalar quantity in mathematics. So now you know what impedance is. But it only applies to clean sine waves? Yes, electrical engineers use them as they are a mathematical representation of alternating current.

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## Application of Complex Numbers (Electrical Engineering)

You'll hear a ton of different terminology, and linear algebra is where you're really slammed with modern mathematical rigor and formalisms. When the complex number is purely imaginary, such as a real part of 0 and an imaginary part of 120, it means the voltage has a potential of 120 volts and a phase of 90Â°, which is physically very real. An imaginary number is a complex number with no real part, such as or. I just use complex numbers every day without thinking about it. Theroot locus,Nyquist plot, andNichols plottechniques all make use of the complex plane. This is exactly what Maxwell's equations do.

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## Basics of Complex Numbers for Electrical Engineers

Impedance allows AC Circuits to be analysed using the usual resistance laws series law, parallel law, etc. . Several methods exist to do this; see methods of contour integration. So the receiver for each point in time have to evaluate the actual value of the signal in that moment but also if the derivative is positive or negative. And thus "complex" representation actually simplifies the maths to deal with physical systems.

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## Why complex numbers are used/introduced in electricity

If I draw a line with a certain length magnitude and angle direction , I have a graphic representation of a complex number which is commonly known in physics as a vector: Figure below A vector has both magnitude and direction Like distances and directions on a map, there must be some common frame of reference for angle figures to have any meaning. In practice you usually just keep track of the electric field and the poynting vector. With two sample streams, each ADC can operate at about halfrate from a single sampler. Arithmetic and logic in computer system Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Deeper analysis of electrical systems requires looking directly at the differential equations.

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## Can Someone Explain how Complex Numbers are Used in Electrical Engineering? : math

The two dimensions, length and angle, allows us to calculate amplitude and phase together, and keep them consistent. Resistors, capacitors, and inductors are characterized by their effect on the relationship between the voltage and current. Related Questions Complex numbers are used in electronics and electromagnetism. Although imaginary numbers are not commonly used in daily life, in engineering and physics they are in fact used to represent physical quantities such as impedance of RL, RC, or RLC circuit. This representation is known as the Cartesian form of z. Thanks and regards, Sara Good point.

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## Application of complex number in engineering

This then produces a two dimensional complex plane with four distinct quadrants labelled, QI, QII, QIII, and QIV. The math could be performed with sin and cos, but if you used Euler's formula and work in the complex plane, the math becomes 50% simpler. I have done some research concerning impedances and understand how they are written in complex form, however I am still confused why complex numbers are necessary in this field over regular numbers. The conjugate of a complex number is an important element used in Electrical Engineering to determine the apparent power of an AC circuit using rectangular form. Then angles between 0 and 90 o will be in the first quadrant I , angles Î¸ between 90 and 180 o in the second quadrant II. This website is a very good resource and will do a good job at explaining these concepts.

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## Why are imaginary numbers used in electrical engineering

The only difference is in multiplication because two imaginary numbers multiplied together becomes a negative real number. Now you can perform arithmetic on electrical circuit by manipulating complex numbers. What are imaginary and complex numbers? However, as an example in rectangular form lets find the value of vector A divided by vector B. Calculating with Complex Numbers Adding and subtracting complex numbers expressed in Cartesian form is quite easy: You add subtract the real parts and imaginary parts separately. Thus, complex conjugates can be thought of as a reflection of a complex number. The key thing is that the eigenvectors of all LTI systems are complex exponentials.

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## math

So complex numbers are absolutely crucial to understanding modern applications of electricity. As I understand it the imaginary part of inductors and capacitors is the side to side motion of the jump rope, whereas the real plane is the straight up and down motion of the wave. This allows the analyst to use precisely the same procedures for modeling passive AC circuits as are used in resistive circuits: the methods are all algebraic. And slide 12-13: "And complex numbers have been VERY convenient to use in the mathematical analysis of electric circuits since then" Treefarmer : I use a picture like yours to illustrate Euler's equation in slide 1 and 6 WFla : to conclude, slide 14, I used the analogy and figure you gave me, and the loved it! The perpendicular imaginary axis is not really in the 3d space we live in. Why do engineers use complex numbers? Are imaginary numbers used in engineering? This should give you a basic understanding of where the complex numbers are coming from.

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