document.write( "Question 1050430: Simplify (i+1)^3200-(i-1)^3200 \n" ); document.write( "
Algebra.Com's Answer #665998 by ikleyn(52878)\"\" \"About 
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document.write( "i + 1 = \"sqrt%282%29%2A%28%28sqrt%282%29%2F2%29+%2B+i%2A%28sqrt%282%29%2F2%29%29\" = \"sqrt%282%29%2A%28cos%28pi%2F4%29+%2B+i%2Asin%28pi%2F4%29%29\".\r\n" );
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document.write( "Now apply de Moivre's formula:  \"%28r%2A%28cos%28alpha%29+%2B+i%2Asin%28alpha%29%29%29%5En\" = \"r%5En%2A%28cos%28n%2Aalpha%29+%2B+i%2Asin%28n%2Aalpha%29%29\".\r\n" );
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document.write( "You will get\r\n" );
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document.write( "\"%28i%2B1%29%5E3200\" =  = \"2%5E1600%2A%28cos%28800%2Api%29+%2B+i%2Asin%28800%2Api%29%29\" = \"2%5E1600\".    (1)\r\n" );
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document.write( "Similarly, \r\n" );
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document.write( "i - 1 = \"sqrt%282%29%2A%28%28sqrt%282%29%2F2%29+-+i%2A%28sqrt%282%29%2F2%29%29\" = \"sqrt%282%29%2A%28cos%28pi%2F4%29+-+i%2Asin%28pi%2F4%29%29\".\r\n" );
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document.write( "\"%28i-1%29%5E3200\" =  = \"2%5E1600%2A%28cos%28800%2Api%29+-+i%2Asin%28800%2Api%29%29\" = \"2%5E1600\".    (2)\r\n" );
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document.write( "Combining (1) and (2), you will get\r\n" );
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document.write( "(i+1)^3200-(i-1)^3200 = \"2%5E1600\" - \"2%5E1600\" = 0.\r\n" );
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document.write( "Answer.  (i+1)^3200-(i-1)^3200 = 0.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is a bunch of my lessons on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Complex numbers and arithmetical operations on them\r
\n" ); document.write( "\n" ); document.write( "    - Complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Addition and subtraction of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Multiplication and division of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Raising a complex number to an integer power\r
\n" ); document.write( "\n" ); document.write( "    - How to take a root of a complex number\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the quadratic equation with real coefficients on complex domain\r
\n" ); document.write( "\n" ); document.write( "    - How to take a square root of a complex number\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the quadratic equation with complex coefficients on complex domain\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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