Period of Complex Exponential Function/Proof 1

Theorem

$\map \exp {z + 2 k \pi i} = \map \exp z$


Proof

\(\ds \map \exp {z + 2 k \pi i}\) \(=\) \(\ds \map \exp z \, \map \exp {2 k \pi i}\) Exponential of Sum: Complex Numbers
\(\ds \) \(=\) \(\ds \map \exp z \times 1\) Euler's Formula Example: $e^{2 k i \pi}$
\(\ds \) \(=\) \(\ds \map \exp z\)

$\blacksquare$


Sources

  • 2001: Christian Berg: Kompleks funktionsteori: $\S 1.5$
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