grandes-ecoles 2013 QI.B

grandes-ecoles · France · centrale-maths2__psi Complex numbers 2 Complex Function Evaluation and Algebraic Manipulation
Let $z \in \mathbb{C}$. We set $z = a + ib$, where $a, b \in \mathbb{R}$.
Deduce that $$\lim_{n \rightarrow \infty} \left(1 + \frac{z}{n}\right)^n = e^z$$
Let $z \in \mathbb{C}$. We set $z = a + ib$, where $a, b \in \mathbb{R}$.

Deduce that
$$\lim_{n \rightarrow \infty} \left(1 + \frac{z}{n}\right)^n = e^z$$