document.write( "Question 987077: 4th root of -256 \n" ); document.write( "
Algebra.Com's Answer #607871 by ikleyn(52776)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Notice that     -256 = 256(cos(180°) + i*sin(180°))   and   256 = \"4%5E4\".\r
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\n" ); document.write( "\n" ); document.write( "The roots of degree  4  of  -256  are  4  complex numbers\r
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\n" ); document.write( "\n" ); document.write( "1)  4(cos(45°) + i*sin(45°)) = \"4%28sqrt%282%29%2F2+%2B+i%2A%28sqrt%282%29%2F2%29%29\" = \"2sqrt%282%29+%2B+2sqrt%282%29%2Ai\";                                                                         (Notice that 45° = 180°/4)\r
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\n" ); document.write( "\n" ); document.write( "2)  4(cos(45°+90°) + i*sin(45°+90°)) = 4(cos(135°) + i*sin(135°)) = \"-4%2Asqrt%282%29%2F2+%2B+%28%284%2Asqrt%282%29%29%2F2%29%2Ai\" = \"-2sqrt%282%29+%2B+2sqrt%282%29%2Ai\";         (Notice that 90° = 360°/4)\r
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\n" ); document.write( "\n" ); document.write( "3)  4(cos(45°+180°) + i*sin(45°+180°)) = 4(cos(225°) + i*sin(225°)) = \"-4%2Asqrt%282%29%2F2+-+%284%2Asqrt%282%29%2F2%29%2Ai\" = \"-2sqrt%282%29+-+2sqrt%282%29%2Ai\";\r
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\n" ); document.write( "\n" ); document.write( "4)  4(cos(45°+270°) + i*sin(45°+270°)) = 4(cos(315°) + i*sin(315°)) = \"4%2Asqrt%282%29%2F2+-+%284%2Asqrt%282%29%2F2%29%2Ai\" = \"2sqrt%282%29+-+2sqrt%282%29%2Ai\".\r
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\n" ); document.write( "\n" ); document.write( "If you want to see my lessons on complex numbers in this site,  look in this \r
\n" ); document.write( "\n" ); document.write( "    - REVIEW of lessons on complex numbers\r
\n" ); document.write( "\n" ); document.write( "and especially in this one \r
\n" ); document.write( "\n" ); document.write( "    - How to take a root of a complex number.\r
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