Eli5 Why do we need complex numbers in real life?

Question

Eli5 Why do we need complex numbers in real life?

In: 11

Answer 1

Because complex numbers make solutions easier. For example, the first year physics students will understand, is a driven and damped oscillator. To mathematically describe it, we use complex exponentials to avoid a lot of trig identities, which then gives us a solution that can be physically interpreted. Of course the complex numbers have no physical meaning, since the first thing we do is we only consider the “real component” of the solution.