document.write( "Question 742206: 4-i over
\n" ); document.write( "2-6i\r
\n" ); document.write( "\n" ); document.write( "can you walk me through the steps Im a little rusty.
\n" ); document.write( "This is what I got.
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Algebra.Com's Answer #852613 by ikleyn(53313) $\"\"$ $\"About$

You can put this solution on YOUR website!
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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( "    (4-i)*(2+6i) = 8 -2i + 24i - 6i^2 = 8 + 22i - 6*(-1) = 8 + 6 + 22i = 14 + 22i.\r\n" );
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document.write( "In the denominator, you have the product of a complex number (2-6i) and its conjugate (2+6i),\r\n" );
document.write( "which is a real number\r\n" );
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document.write( "    (2-6i)*(2+6i) = 2^2 + 6^2 = 4 + 36 = 40.\r\n" );
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document.write( "Thus, the ratio    is\r\n" );
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document.write( "     =  = .\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,   = 0.35 + 0.55*i.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The answer in the post by @lynnlo is incorrect.\r
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