Euler’s Formula

Let $\theta \in \mathbb{R}$. Then $e^{j\theta }=\cos \theta +j\sin \theta$

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 $\cos (\theta )$ and $\sin (\theta )$ as: $\sin (\theta )=\frac{e^{i\theta }-e^{-i\theta }}{2i}$ $\cos (\theta )=\frac{e^{i\theta }+e^{-i\theta }}{2}$

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.

Related

• Hyperbolic Function