04 - Principals

Principal Value

Values $\theta \in (-\pi ,\pi ]$ such that

$$z=|z|e^{i\theta }$$

Principal Value of Logarithm

$\mathrm{Log}$ used in Log function

Principal Value of $z^{\alpha }$

Let $\alpha ,z\in \mathbb{C}$ and $z\ne 0$ then

Principal Value of $z^{\alpha }$ is

$$\exp (\alpha \mathrm{Log}(z))$$

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