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