If it doesn’t exist, why and how do we use it?
In: Mathematics
Imaginary numbers are used extensively in electrical engineering.
Electrical engineering for AC circuits deals with sinusoidal (cosine and sine) waves. The math for sinusoidal waves can be greatly simplified by using a combination of real and imaginary numbers.
E.g., when an AC voltage is applied to a resistor, the current and voltage have the same phase, that is they are perfectly aligned. If a capacitor is added to the circuit, the current and voltage become out of phase.
The mathematical representation of the phase difference using sine functions is complicated, time consuming and confusing. Simple operations like addition are a nightmare.
Representing the phase difference by using a combination of real and imaginary numbers greatly simplifies the math. After a short while, a person can develop an intuitive understanding of electricity in circuits by using imaginary numbers as a reference.
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