Complex Polar Notation

Complex Polar Notation

(1)
\begin{align} i=e^{i{\pi}/2} \end{align}
(2)
\begin{align} i^2=e^{i{\pi}} \end{align}
(3)
\begin{align} i^3=e^{i3{\pi}/2} \end{align}
(4)
\begin{align} ie^{i\theta}=e^{i(\theta+pi/2)} \end{align}
(5)
\begin{align} r_1e^{i\alpha}*r_2e^{i\beta}=r_1*r_2e^{i(\alpha+\beta)} \end{align}
(6)
\begin{align} ire^{i\theta}=e^{i\theta/2}*re^{i\theta}=re^{i(\theta+pi/2)} \end{align}
(7)
\begin{align} \frac{d}{dt}(re^{i\theta})=\frac{d}{dt}(r)e^{i\theta}+\frac{d}{dt}(\theta)ie^{i\theta} \end{align}