# Multiple values of complex power of a complex number

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.