Euler's Formula/Examples/e^2 i pi
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Example of Use of Euler's Formula
- $e^{2 i \pi} = 1$
Proof
| \(\ds e^{2 i \pi}\) | \(=\) | \(\ds \cos 2 \pi + i \sin 2 \pi\) | Euler's Formula | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1 + i \times 0\) | Cosine of $2 \pi$, Sine of $2 \pi$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations: $(2.19)$
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 4.5$. The Functions $e^z$, $\cos z$, $\sin z$: $\text{(ii)}$