---
tag: 0RNGDMHT7M
kind: concept
name: Complex power
aliases: [complex-exponentiation, cpow]
msc: [33B10]
sources:
  - url: https://en.wikipedia.org/wiki/Exponentiation
    locator: Complex exponentiation
---

## Summary

A complex power $z^w$ with $z \neq 0$ is a number $e^{w \ell}$ where $\ell$ is a logarithm of $z$, see the [[definition|0ZV9A7EV0F]].
The principal value is $e^{w \operatorname{Log} z}$.