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
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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
Last edited by sa-ri-ga-ma; May 5th 2010 at 04:57 PM.
$\displaystyle (-6 + 6i)^4 = 6^4(-1+i)^4 = 6^4(cos 3\pi/4 + i sin 3 \pi/4)^4 = $ $\displaystyle 6^4(cos 3\pi + i sin 3\pi) = 6^4 (-1) = -(6^4).$
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