Logarithm of a complex number

Theorem

Let $z \in \mathbb{C}$ written in polar form $z=Re^{i\theta}$ with $-\pi < \theta \leq \pi$. Then $$\log(z) = \log(R) + i \theta,$$ where $\log$ denotes the logarithm, $i$ denotes the imaginary number, and $\log(R)$ is computed using the integral definition.