Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard natural complex exponential function is the D4881: Complex function \begin{equation} \exp : \mathbb{C} \to \mathbb{C} \setminus \{ 0 \}, \quad \exp(z) = \lim_{N \to \infty} \sum_{n = 0}^N \frac{z^n}{n!} \end{equation}

Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard natural complex exponential function is the D4881: Complex function \begin{equation} \exp : \mathbb{C} \to \mathbb{C} \setminus \{ 0 \}, \quad \exp(z) = \sum_{n = 0}^{\infty} \frac{z^n}{n!} \end{equation}

Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard natural complex exponential function is the D4881: Complex function \begin{equation} \exp : \mathbb{C} \to \mathbb{C} \setminus \{ 0 \}, \quad \exp(z) = \frac{z^0}{0!} + \frac{z^1}{1!} + \frac{z^2}{2!} + \frac{z^3}{3!} + \cdots \end{equation}