[[Mathematics MOC]]
# Euler's formula

**Euler's formula** states #m/thm/complex
$$
\begin{align*}
e^{i\theta} = \cos\theta + i \sin\theta
\end{align*}
$$
giving a convenient notation for denoting complex numbers radially.
It follows
$$
\begin{align*}
\cos\theta &= \frac{1}{2}\left( e^{i \theta} + e^{-i\theta} \right) \\
\sin\theta &= \frac{1}{2i} \left( e^{i\theta} - e^{-i\theta} \right) 
\end{align*}
$$

> [!missing]- Proof
> #missing/proof


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