document.write( "Question 1184218: If \"+%283%2F2+%2B+isqrt%283%29%2F2%29%5E50+=+3%5E25%28x+%2B+iy%29+\" where x and y are real numbers then find x and y?
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Algebra.Com's Answer #814767 by ikleyn(52878)\"\" \"About 
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\n" ); document.write( "If \"+%283%2F2+%2B+isqrt%283%29%2F2%29%5E50+=+3%5E25%28x+%2B+iy%29+\" where x and y are real numbers then find x and y?
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document.write( "The number  \"3%2F2+%2B+i%2A%28sqrt%283%29%2F2%29\"  has the modulus  r = \"sqrt%28%283%2F2%29%5E2+%2B+3%2F4%29\" = \"sqrt%289%2F4+%2B+3%2F4%29\" = \"sqrt%2812%2F4%29\" = \"sqrt%283%29\"\r\n" );
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document.write( "                        and the argument  a = \"pi%2F6\".\r\n" );
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document.write( "THEREFORE,  \"3%2F2+%2B+i%2A%28sqrt%283%29%2F2%29\" = \"sqrt%283%29%2Acis%28pi%2F6%29\".\r\n" );
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document.write( "Hence,  the left side number  \"%283%2F2+%2B+isqrt%283%29%2F2%29%5E50\" is equal to  \"%28sqrt%283%29%29%5E50%2Acis%2850pi%2F6%29\" = \"3%5E25%2Acis%282pi%2F6%29\" = \"3%5E25%2Acis%28pi%2F3%29\".\r\n" );
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document.write( "It implies that  x + iy = \"cis%28pi%2F3%29\" = \"1%2F2+%2B+i%2A%28sqrt%283%29%2F2%29\".\r\n" );
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document.write( "So  x = \"1%2F2\",  y = \"sqrt%283%29%2F2\".      ANSWER\r\n" );
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