Question

How are imaginary numbers used in real life$?$

Answer 1

Imaginary numbers or complex numbers are used in various fields such as:

1. Signal processing: Imaginary numbers can also be applied to signal processing, which is useful in cellular technology and wireless technologies, as well as radar and even biology (brain waves). Essentially, if what is being measured relies on a sine or cosine wave, the imaginary number is used.
2. AC circuit analysis: Imaginary numbers are particularly applicable in electricity, specifically alternating current (AC) electronics. AC electricity changes between positive and negative in a sine wave. Combining AC currents can be very difficult because they may not match properly on the waves. Using imaginary currents and real numbers helps those working with AC electricity do the calculations and avoid electrocution.
3. Quantum Mechanics: A wave function, simply put, is a complex probability distribution indicating the possible position of a particle on a specific time.