What is the use of $i=\sqrt{-1}$ in plane wave equation?

Question

I mean we can represent plane waves using just sine and cosine functions. Why do we need to use Euler's formula to represents plane waves as complex exponentials? What is the intuition behind using $i=\sqrt{-1}$. Of course, the plane waves are solution of Maxwell's electromagnetic equations.

Please clarify my doubt!

Does this answer your question? Electromagnetic waves - complex numbers — Thomas Fritsch, Sep 20 '20 at 14:17

score 1 · Answer 1 · answered Sep 20 '20 at 14:17

İnitially Euler's formula shortens the wave function and also it's multiplicative property for the powers of e allows simplifications in trigonometrical calculations in addition to that several types of wave envelopes (Gaussian) are easy to represent in the complex exponential form and to get necessary part simply look at its complex and imaginary parts.

What is the use of $i=\sqrt{-1}$ in plane wave equation?

1 Answers1