Math in Engineering

Electrical Engineeringand Materials Science

How are imaginary numbers used in electrical engineering?

Imaginary numbers are used in electrical engineering because complex numbers are an integral part of electrical problems. In fact, there are often more imaginary numbers in electrical engineering problems than there are real numbers. This is because a complex number is a pair of numbers in which one number is real, the other imaginary (or a real number multiplied by the value i, defined as the square root of -1; for more information about imaginary numbers, see “Math Basics”).

For instance, we know electricity flows through an electrical circuit component such as a light bulb. The bulb actually resists the flow of some electricity by doing work—or shining—thus, the current is real and measured by a current meter. But if the current can’t flow through a device, the current becomes imaginary. For example, a capacitor is two pieces of metal that do not touch; therefore, if one adds a voltage, no real current can flow through it.


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