Euler's Formula/Examples

Examples of Use of Euler's Formula

Example: $e^{i \pi / 4}$

$e^{i \pi / 4} = \dfrac {1 + i} {\sqrt 2}$


Example: $e^{i \pi / 2}$

$e^{i \pi / 2} = i$


Example: $e^{-i \pi / 2}$

$e^{-i \pi / 2} = -i$


Example: $e^{i \pi}$

$e^{i \pi} = -1$


Example: $e^{2 i \pi}$

$e^{2 i \pi} = 1$


Example: $e^{2 k i \pi}$

$\forall k \in \Z: e^{2 k i \pi} = 1$
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