Complex (and thus imaginary) numbers are used by many people in various fields. The most logical is in the field of mathematics: In algebra, complex numbers give mathematicians a way to find the roots of polynomials.

Engineers and scientists also often need to use complex numbers. Because such applications are based on polynomial models in theory, complex numbers are needed. For example, circuit theory has polynomials as part of the model equation for simple circuits. Vibrations with wavelike results in mechanical engineering are also connected to the use of complex numbers. And even in physics, quantum mechanics uses complex numbers for just about everything. The wave functions of particles that have a complex amplitude include real and “imaginary” parts—both of which are essential to the computations.

Complex numbers are also used by musicians, economists, and stockbrokers as well. And indirectly, everyone who has to deal with light switches, loudspeakers, electric motors, and sundry other mechanical devices uses imaginary numbers just by using things that were engineered through the use of imaginary numbers.