Why is $\left\lvert e^{i\Im(s)\log(n)}\right\rvert = 1$

Question

Where $n \in \mathbb{N}$ and $s \in \mathbb{C}$.

Answer 1

Recall $e^{ix} = \cos x + i \sin x$. So if $x$ is real, then $|e^{ix}| = (\cos^2 x + \sin^2 x)^{1/2} = 1$.