document.write( "Question 1205500: If let z= x+ iy , |z|= 8 then value of |(conj(z)+48)/(3z + 4)|=.....
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Algebra.Com's Answer #842354 by Edwin McCravy(20056) $\"\"$ $\"About$

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If let z= x+ iy , |z|= 8 then value of |(conj(z)+48)/(3z + 4)|=.....
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document.write( "This is a multiple-choice problem with 4 potential answers.\r\n" );
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document.write( "So, it must be true that the answer is the same no matter what x and y are,\r\n" );
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document.write( "as long as |z| = |x+iy| = 8\r\n" );
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document.write( "That's because your teacher couldn't have given you only 4 numerical choices if\r\n" );
document.write( "there could be different values for different values of x and y.\r\n" );
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document.write( "So, instead of bothering to prove it for all values of x and y, just choose this\r\n" );
document.write( "easy case:\r\n" );
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document.write( "x=8, y=0, then z = 8+0i = 8-0i = conj(8+0i) = 8, then\r\n" );
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document.write( "|(conj(z)+48)/(3z + 4)| = |8+48)/[(3)(8) + 4]| = |56/28| = |2| = 2.\r\n" );
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document.write( "So the answer is 2. \r\n" );
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document.write( "Note: if your problem had been stated this way: \r\n" );
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document.write( "if |z| = 8 then prove that the value of |(conj(z)+48)/(3z + 4)| = 2,\r\n" );
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document.write( "then there would be a lot more work.  So be on the lookout for multiple\r\n" );
document.write( "choice questions like this with variables which have no variables in the\r\n" );
document.write( "choices.  For if you run into such a problem, just substitute easy numbers\r\n" );
document.write( "for the variables and whatever you get will bound to be the correct answer.\r\n" );
document.write( "You'll save lots of time.\r\n" );
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document.write( "Edwin

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