DeMoivre's Theorem

**Nessa214** · May 4th 2010, 04:55 PM

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

**sa-ri-ga-ma** · May 4th 2010, 05:40 PM

Originally Posted by Nessa214

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

(-6 + 6i ) ^4 = 6^4(-1 + i)^4 = 2^2*6^4(cos3π/4 + sin3π/4)^4 = 4* 6^4(cos3π + sin3) = -4*6^4

**ebaines** · May 5th 2010, 10:50 AM

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

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