Question

Convert the complex number z = -12 + 5i from rectangular form to polar form.​

Answer 1

Answer:

$z=13(\cos 157\degree +i\sin157\degree)$

Step-by-step explanation:

The given complex number is

$z=-12+5i$

The polar form of this complex number is;

$z=r(\cos \theta +i\sin \theta)$, where

$r=\sqrt{(-12)^2+5^2}$

$r=\sqrt{144+25}=\sqrt{169}=13$

and

$\theta =\tan^{-1}(\frac{5}{-12})$

This implies that;

$\theta=157\degree$ to the nearest degree.

Hence the polar form is

$z=13(\cos 157\degree +i\sin157\degree)$