Euler's Formula/Examples/e^2 i pi

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 $e^z$, $\cos z$, $\sin z$: $\text{(ii)}$
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