# Thread: Calculating in polar form when given complex numbers

1. ## Calculating in polar form when given complex numbers

Hey,

I have the following problem that I am supposed to solve.

(2+7i)^12/(4-i)^11

I know how to find the radius, but the angle part is troubling me. I know its arctan(number1/number2). But how do I find out number1 and number2?

Any help would be much appreciated!

2. Start by finding..

$
\frac{(2+7i)^{12}}{(4-i)^{11}} = \frac{\sqrt{2^2+7^2}\text{cis}\left(12 \tan^{-1}\left(\frac{7}{2}\right)\right)}{\sqrt{4^2+(-1)^2}\text{cis}\left(11 \tan^{-1}\left(\frac{-1}{4}\right)\right)}
$

Once these are in polar form $z_1 = r_1 \times \text{cis}\theta_1$ and $z_2 = r_2 \times \text{cis}\theta_2$

then

$\frac{z_1}{z_2} = \frac{r_1}{r_2}\text{cis}(\theta_1 - \theta_2)$