Euler's Formula/Examples/e^i pi
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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: $(2.19)$