document.write( "Question 594364: (3-2i)^6
\n" ); document.write( "Im not looking for the answer just the how to get to the answer. \n" ); document.write( "

Algebra.Com's Answer #376708 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
(3-2i)^6
\n" ); document.write( "Im not looking for the answer just the how to get to the answer.
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\n" ); document.write( "One way is to multiply it. Square it, then cube the result.
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\n" ); document.write( "If it's a larger exponent, that's not practical, so use DeMoivre's Theorem.
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\n" ); document.write( " $\"Magnitude+=+sqrt%283%5E2+%2B+2%5E2%29+=+sqrt%2813%29\"$
\n" ); document.write( "Angle = arctan(-2/3)
\n" ); document.write( "sin(A) = -2/sqrt(13)
\n" ); document.write( "cos(A) = 3/sqrt(13)
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\n" ); document.write( "--> z = sqrt(13)*cis(A)
\n" ); document.write( "z^6 = (sqrt(13))^6*cis(6A)
\n" ); document.write( "= 13^3*cis(6A)
\n" ); document.write( "= 2197*(-0.92626 + i*0.37688)
\n" ); document.write( "= -2035 + 828i
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\n" ); document.write( "It's the same answer I get using an Excel sheet I made to do these.
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