Euler's Formula/Examples
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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: $e^{2 k i \pi}$
- $\forall k \in \Z: e^{2 k i \pi} = 1$