Theory

Theory 1

The exponential notation leads to a formula for a complex root of any complex number:

Every complex number actually has distinct complex roots!

That’s two square roots, three cube roots, four roots, etc.

All complex roots

The complex roots of are given by:

In Cartesian notation:

In words:

• Start with the basic root:
• Rotate by increments of to get all other roots

Extra - Complex roots proof

We must verify that :