document.write( "Question 1180532: Find the 3 cube roots of -8 in polar form. \n" ); document.write( "

Algebra.Com's Answer #810236 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the 3 cube roots of -8 in polar form.
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document.write( "-8 = -8+0i\r\n" );
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document.write( "Graph the vector whose magnitude (modulus) is r=8, whose tail is at (0,0),\r\n" );
document.write( "and whose tip is at (-8,0), and whose argument (angle) is θ=180^o. \r\n" );
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document.write( "Since the cube root is the 1/3 power:\r\n" );
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document.write( "We raise everything to the 1/3 power.  In doing so we will use deMoivre's\r\n" );
document.write( "theorem, where we raise the magnitude (modulus 8) to the 1/3 power (i.e.,\r\n" );
document.write( "take its cube root 2), and multiply its argument (angle) by 1/3.\r\n" );
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document.write( "Now, since there are 3 cube roots, we take three consecutive integers for n.\r\n" );
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document.write( "Let n=0\r\n" );
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document.write( "Let n=1\r\n" );
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document.write( "Let n=2\r\n" );
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document.write( "[Notice that the second one would turn out to be 2(-1+0i) or just -2, which\r\n" );
document.write( "is the real cube root of -8.]\r\n" );
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document.write( "Edwin

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