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