Question 594364
(3-2i)^6
Im not looking for the answer just the how to get to the answer.
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One way is to multiply it.  Square it, then cube the result.
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If it's a larger exponent, that's not practical, so use DeMoivre's Theorem.
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{{{Magnitude = sqrt(3^2 + 2^2) = sqrt(13)}}}
Angle = arctan(-2/3)
sin(A) = -2/sqrt(13)
cos(A) = 3/sqrt(13)
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--> z = sqrt(13)*cis(A)
z^6 = (sqrt(13))^6*cis(6A)
= 13^3*cis(6A)
= 2197*(-0.92626 + i*0.37688)
= -2035 + 828i
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It's the same answer I get using an Excel sheet I made to do these.