Theory

Theory 1

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

distinct roots

Every complex number actually has distinct roots!

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

All complex roots

The complex roots of are given by this formula:

In Cartesian notation:

In words:

• Start with the basic root:
• Rotate by increments of to get all other roots
  • After distinct roots, this process repeats itself

Extra - Complex roots proof

We must verify that :