The [[Complex Numbers|Complex]] [[Exponential]] is an extension of the definition for exponentiating on the [[Real Numbers|reals]]. $\huge e^{i\theta} = \cos\theta+i\sin\theta $ $\huge \begin{align} e^{x} &= 1+x+\frac{x^{2}}{2} + \frac{x^{3}}{6} + \cdots \\ &= \sum^{\infty}_{n=0} \frac{x^{n}}{n!} \end{align} $