Euler's Formula/Examples/e^i pi

Example of Use of Euler's Formula

$e^{i \pi} = -1$


Proof

\(\ds e^{i \pi}\) \(=\) \(\ds \cos \pi + i \sin \pi\) Euler's Formula
\(\ds \) \(=\) \(\ds -1 + i \times 0\) Cosine of $\pi$, Sine of $\pi$
\(\ds \) \(=\) \(\ds -1\)

$\blacksquare$


Also see

This result is significant enough to have its own name: Euler's Identity.


Sources

  • 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations: $(2.19)$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.