# `(3 - 2i)^5` Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

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mathace | Certified Educator

`z=(3-2i)^5`

`r=sqrt[(3)^2+(-2)^2]=sqrt[9+4]=sqrt13`

`theta=arctan(-2/3)=-.5880`

DeMoivre's Theorem

`z^n=[r(costheta+isintheta)]^n=r^n[cosntheta+isinntheta]`

`z^5=[sqrt13(cos(-.5880)+isin(-.5880))]^5`

`z^5=(sqrt13)^5[cos5(-.5880)+isin5(-.5880)]`

`z^5=169sqrt13[cos(-2.94)+isin(-2.94)]`

`z^5=-597.00-122.00i`