Use the DeMoivre's Theorem to find the indicated power of this complex number (-6 + 6i ) ^4

Can someone please show the work for this problem. Thanks in advance (Talking)

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- May 4th 2010, 04:55 PMNessa214DeMoivre's Theorem
Use the DeMoivre's Theorem to find the indicated power of this complex number (-6 + 6i ) ^4

Can someone please show the work for this problem. Thanks in advance (Talking) - May 4th 2010, 05:40 PMsa-ri-ga-ma
- May 5th 2010, 10:50 AMebaines
$\displaystyle (-6 + 6i)^4 = 6^4(-1+i)^4 = 6^4(cos 3\pi/4 + i sin 3 \pi/4)^4 =

$

$\displaystyle

6^4(cos 3\pi + i sin 3\pi) = 6^4 (-1) = -(6^4).$