document.write( "Question 736989: 5-i / 4-3i \n" ); document.write( "

Algebra.Com's Answer #852689 by ikleyn(53313) $\"\"$ $\"About$

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document.write( "You are given a fraction of complex numbers  .\r\n" );
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document.write( "They want you transform it to the standard form complex number.\r\n" );
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document.write( "To do it, multiply the numerator and denominator by the complex number,\r\n" );
document.write( "which is conjugate to the denominator of the given fraction.\r\n" );
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document.write( "So, you write\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "Now, to avoid a mess, let's work with the numerator and the denominator separately.\r\n" );
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document.write( "In the numerator, you have\r\n" );
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document.write( "    (5-i)*(4+3i) = 20 + 15i - 4i - 3i^2 = 20 + 11i - 3*(-1) = 20 + 3 + 11i = 23 + 11i.\r\n" );
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document.write( "In the denominator, you have the product of a complex number (4-3i) and its conjugate (4+3i),\r\n" );
document.write( "which is a real number\r\n" );
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document.write( "    (4-3i)*(4+3i) = 4^2 + 3^2 = 16 + 9 = 25.\r\n" );
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document.write( "Thus, the ratio    is\r\n" );
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document.write( "     =  =  = 0.92 + 0.44i.\r\n" );
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document.write( "It is a standard form of a complex number.\r\n" );
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document.write( "At this point, the assignment is complete.\r\n" );
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document.write( "ANSWER.   = .\r\n" );
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document.write( "         Or, which is the same,   = 0.92 + 0.44*i.\r\n" );
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