Difference between revisions of "Real and imaginary parts of log"

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(Created page with "==Theorem== Write $z \in \mathbb{C}$ using polar coordinates: $z=x+iy=re^{i\theta}$. The following formula holds for $-\pi < \mathrm{arg}(z) \leq \pi$: $$\log(z)=\log(r)+i...")
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Revision as of 05:52, 4 June 2016

Theorem

Write $z \in \mathbb{C}$ using polar coordinates: $z=x+iy=re^{i\theta}$. The following formula holds for $-\pi < \mathrm{arg}(z) \leq \pi$: $$\log(z)=\log(r)+i\theta,$$ where $\mathrm{arg}$ denotes the argument and $\log$ denotes the logarithm.

Proof

References