`(sqrt(5) - 4i)^3` Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

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`z=(sqrt5-4i)^3`

`r=sqrt[sqrt5^2+(-4)^2]=sqrt[5+16)=sqrt(21)`

`theta=arctan(-4/sqrt5)=-1.0610`

DeMoivre's Theorem

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

`z^3=[sqrt21(cos(-1.0610)+isin(-1.0610))]^3`

`z^3=(sqrt21)^3[cos3(-1.0610)+isin3(-1.0610)]`

`z^3=21sqrt21[cos(-3.183)+isin(-3.183)]`

`z^3=-96.15+4.00i`

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