document.write( "Question 1170521: Find the four fourth roots of z=16(cos 4pi/3 + i sin 4pi/3) Write each root in standard form.\r
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Algebra.Com's Answer #795406 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
Noting that a $\"2pi\"$ rotation doesn't change things, we can express z in polar form:
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\n" ); document.write( "\n" ); document.write( "Now finding the four 4th roots is nearly trivial (4th root of 16 is 2, then just divide exponents by 4). You must let n=0,1,2, and 3 to get the four 4th roots:

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= 2(0.5 + i*0.866) = $\"highlight%281+%2B+i%2A1.732%29+\"$
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\n" ); document.write( "NOTE that $\"z%5B0%5D\"$ is also called the principal root
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\n" ); document.write( "\n" ); document.write( "Now set n=1 to find the 2nd root\r
\n" ); document.write( "\n" ); document.write( "n=1:

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\n" ); document.write( "\n" ); document.write( "That exponent works out to $\"+5pi%2F6+\"$ :\r
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= $\"+highlight%28-1.732+%2B+i%2A1%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let n=2 then n=3 to get the remaining two roots. You should get:
\n" ); document.write( "n=2: $\"+z%5B2%5D+=+2%2A%28cos%28%284pi%29%2F3%29+%2B+i%2Asin%28%284pi%29%2F3%29%29%29+\"$
\n" ); document.write( "n=3: $\"+z%5B3%5D+=+2%2A%28cos%28%2811pi%29%2F6%29+%2B+i%2Asin%28%2811pi%29%2F6%29%29%29+\"$ \r
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