Let $z \in \mathbb{C}$. We set $z = a + ib$, where $a, b \in \mathbb{R}$. Let $n \in \mathbb{N}^*$. Determine the modulus and an argument of $\left(1 + \frac{z}{n}\right)^n$ as a function of $a$, $b$ and $n$.
Let $z \in \mathbb{C}$. We set $z = a + ib$, where $a, b \in \mathbb{R}$.
Let $n \in \mathbb{N}^*$. Determine the modulus and an argument of $\left(1 + \frac{z}{n}\right)^n$ as a function of $a$, $b$ and $n$.