📂Complex Anaylsis

The Exponential Function as a Conformal Mapping

Theorem ¹

The conformal mapping $w = f(z) = e^{z} = e^{x} e^{i y}$ maps a rectangle to a sector or an annulus.

Explanation

$f(z) = e^{z}$ is clearly a conformal mapping, but it is not injective, so various restrictions are needed when considering its inverse mapping.