HW1 Problem 8

Write the complex number $12+5i$ in polar form $|z|(p+qi)$where $|p+qi|=1$.
$\because z=12+5i$ $\therefore |z|=\sqrt{12^2+5^2}=13$
$\because z=|z|(\cos\theta+\sin\theta)$ $\therefore z=12+5i=13(\cos\theta+\sin\theta)$
$\therefore 12=13\cos\theta , 5=13\sin\theta$ namely, $\cos\theta=\frac{12}{13}, \sin\theta=\frac{5}{13}$ $\therefore z=12+5i=13(\frac{12}{13}+\frac{5}{13}i)$