document.write( "Question 325079: (-16)^1/4 how do I evaluate this expression \n" ); document.write( "

Algebra.Com's Answer #232786 by Alan3354(69443) $\"\"$ $\"About$

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(-16)^1/4 how do I evaluate this expression
\n" ); document.write( "= $\"%281%2F16%29%5E%281%2F4%29\"$
\n" ); document.write( "= $\"sqrt%28sqrt%28-16%29%29\"$
\n" ); document.write( "= $\"sqrt%284i%29\"$ and $\"sqrt%28-4i%29\"$
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\n" ); document.write( "A better method:
\n" ); document.write( "-16 = 16cis(180 + n*360)
\n" ); document.write( "(16cis(180+n*360))^(1/4) = 2cis(45+n*90)
\n" ); document.write( "= 2cos(45) + 2i*sin(45) = sqrt(2) + i*sqrt(2)
\n" ); document.write( "= 2cos(135) + 2i*sin(135) = -sqrt(2) + i*sqrt(2)
\n" ); document.write( "= 2cos(225) + 2i*sin(225) = -sqrt(2) - i*sqrt(2)
\n" ); document.write( "= 2cos(315) + 2i*sin(315) = +sqrt(2) - i*sqrt(2)
\n" ); document.write( "4th root, 4 answers above.
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