Math Help - DeMoivre's Theorem

1. DeMoivre'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

2. 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

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

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