Euler's Formula/Corollary

Corollary to Euler's Formula
Let $z \in \C$ be a complex number.

Then:
 * $e^{-i z} = \cos z - i \sin z$

where:
 * $e^{-i z}$ denotes the complex exponential function
 * $\cos z$ denotes the complex cosine function
 * $\sin z$ denotes complex sine function
 * $i$ denotes the imaginary unit.

Corollary
This result is often presented and proved separately for arguments in the real domain: