8 - The Exponential Form Of Complex Numbers

Also known as Euler's Form, this form stems from Euler's expansion of the function to any complex number. We won't get into the mechanisms behind that because it's too advanced.

All you need to know is the reasoning behind it.

For any real number x, can be expressed as
As a consequence, we can express any polar form as an easy exponential form:

The advantages of the Exponential Form

We can use the exponential form to easily compute multiples and powers of complex numbers.

8 - The Exponential Form Of Complex Numbers

The advantages of the Exponential Form

Try it yourself! Let's start with multiplication.

Let's now try powers.

Let's also try division!

It's that easy.

9 - Complex Numbers in The Fundamental Theorem of Algebra