document.write( "Question 1080584: 7. Find the cube roots of 1-i \n" ); document.write( "

Algebra.Com's Answer #694685 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"r=sqrt%281%5E2%2B%28-1%29%5E2%29=sqrt%281%2B1%29=sqrt%282%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"theta=tan%5E%28-1%29%28-1%2F1%29=%287%2F4%29pi\"$
\n" ); document.write( "So then for the cube root, the modulus would be
\n" ); document.write( " $\"root%283%2Csqrt%282%29%29=root%286%2C2%29\"$
\n" ); document.write( "For the angle,
\n" ); document.write( " $\"A%5B1%5D=%281%2F3%29%287%2F4%29pi=%287%2F12%29pi\"$
\n" ); document.write( " $\"A%5B2%5D=%281%2F3%29%287%2F4%29pi%2B1%2A%282pi%29%2F3=%285%2F4%29pi\"$
\n" ); document.write( " $\"A%5B3%5D=%281%2F3%29%287%2F4%29pi%2B2%2A%282pi%29%2F3=%2823%2F12%29pi\"$
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\n" ); document.write( " $\"z%5B1%5D=root%286%2C2%29%2A%28cos%28%287%2F12%29pi%29%2Bi%2Asin%28%287%2F12%29pi%29%29\"$
\n" ); document.write( " $\"z%5B2%5D=root%286%2C2%29%2A%28cos%28%285%2F4%29pi%29%2Bi%2Asin%28%285%2F4%29pi%29%29\"$
\n" ); document.write( " $\"z%5B3%5D=root%286%2C2%29%2A%28cos%28%2823%2F12%29pi%29%2Bi%2Asin%28%2823%2F12%29pi%29%29\"$
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