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Proposition: Functional Equation of the Complex Exponential Function
For all complex numbers \(x,y\in\mathbb C\), the complex exponential function fulfills the following functional equation:
\[\exp(x+y)=\exp(x)\cdot \exp(y).\]
In particular, for any complex number \(z=a+ib\) with the real part \(\Re (z)=a\) and the imaginary part \(\Im (z)=b\), we have
\[\exp(z)=\exp(a+ib)=\exp(a)\cdot \exp(ib).\]
Table of Contents
Proofs: 1 Corollaries: 1
Mentioned in:
Proofs: 1 2 3
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983