Conformal Mapping by Exponential Function 📂Complex Anaylsis

Conformal Mapping by Exponential Function

Theorem ¹

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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 since it is not injective, various restrictions are necessary when considering its inverse mapping.

Osborne (1999). Complex variables and their applications: p217. ↩︎

Conformal Mapping by Exponential Function

Theorem 1

Explanation

Theorem ¹