# Multiple values of complex power of a complex number

- Author:
- Simon Mullen

The definition for the complex power of a complex number is given below.
This definition uses the multi-valued complex natural logarithm which is itself defined by:
for
where is our principal branch defined by:
were is our principal branch of the argument function and is the real nature logarithm.
The complex power is defined by:
where
which gives
for
The red points give are for k positive and the green points are for k negative.
Drag and about to see how all the values of changes.