Complex Numbers Review

Euler formula:

$$\cos \theta +j\sin \theta =e^{j\theta }$$

Euler identity:

$$\begin{array}{rl}\theta & =\pi \\ e^{j\pi }& =\cos \pi +j\sin \pi \\ e^{j\pi }& =-1\\ e^{j\pi }+1& =0\end{array}$$

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$$\begin{array}{r}z=r(\cos \theta +j\sin \theta )=r{e}^{j\theta }\\ z=\mid z\mid e^{j\angle z}\end{array}$$