Question

Express $Z=1+i\sqrt{3}$. in polar form.

Answer 1

$Z=1+i\sqrt{3}=2(\frac{1}{2}+i\frac{\sqrt{3}}{2})...........\left(1\right)$
Let Polar form of Given Equation be $Z=rcos\theta +irsin\theta ...............\left(2\right)$
Comparing (1) and (2)
we can write,
$rcos\theta =2\ast \frac{1}{2}=2\cos {60}^{o}rsin\theta =2\ast \frac{1}{2}=2\sin {60}^o$
$\therefore Z=2(\cos {60}^o+i\sin {60}^o)$