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Math Help - Calculating in polar form when given complex numbers

  1. #1
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    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!
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  2. #2
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    Start by finding..

     <br />
\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)}<br />

    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)
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