# Euler’s Formula

Let $θ∈R$. Then $e_{jθ}=cosθ+jsinθ$

There is also Euler’s Identity, which is different.

We use this for the complex exponential form of Complex Numbers.

So we can write concisely $cos(θ)$ and $sin(θ)$ as: $sin(θ)=2ie_{iθ}−e_{−iθ} $ $cos(θ)=2e_{iθ}+e_{−iθ} $

### Euler’s Formula in MATH239

Euler's Formula (Theorem 7.2.1)

Let $G$ be a Connected Graph with $n$ vertices and $m$ edges. Consider a planar embedding of $G$ with $f$ faces. Then $n−m+f=2$.

The proof for this is done by induction.