document.write( "Question 78176: assignment is to simplify this expression: (3-i)^-2\r
\n" ); document.write( "\n" ); document.write( "i get as far as 1/(9-6i+i^2)\r
\n" ); document.write( "\n" ); document.write( "answers sheet says correct answer is (4+3i)/50\r
\n" ); document.write( "\n" ); document.write( "can you help me figure out how to get that answer?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #56085 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%283-i%29%5E-2\"$ Start with the given expression
\n" ); document.write( " $\"1%2F%283-i%29%5E2\"$ Invert
\n" ); document.write( " $\"1%2F%289-6i%2Bi%5E2%29\"$ Foil
\n" ); document.write( " $\"1%2F%289-6i%2B-1%29\"$ replace $\"i%5E2\"$ with (-1) Since $\"i=sqrt%28-1%29\"$ $\"i%5E2=-1\"$
\n" ); document.write( " $\"1%2F%288-6i%29\"$ Combine like terms
\n" ); document.write( " $\"%281%2F%288-6i%29%29%28%288%2B6i%29%2F%288%2B6i%29%29\"$ Multiply the numerator and denominator by the complex conjugate $\"8%2B6i\"$ this will rationalize the denominator (ie it will get rid of the i term in the denominator)
\n" ); document.write( " $\"%288%2B6i%29%2F%28%288-6i%29%288%2B6i%29%29\"$ Multiply
\n" ); document.write( " $\"%288%2B6i%29%2F%2864%2Bcross%2848i-48i%29-36i%5E2%29\"$ Foil
\n" ); document.write( " $\"%288%2B6i%29%2F%2864-36i%5E2%29\"$ Combine like terms
\n" ); document.write( " $\"%288%2B6i%29%2F%2864-36%28-1%29%29\"$ Replace $\"i%5E2\"$ with (-1)
\n" ); document.write( " $\"%288%2B6i%29%2F%2864%2B36%29\"$ Multiply -36 by -1
\n" ); document.write( " $\"%288%2B6i%29%2F100\"$ Combine like terms
\n" ); document.write( " $\"2%284%2B3i%29%2F100\"$ Factor out a 2
\n" ); document.write( " $\"%284%2B3i%29%2F50\"$ Divide \n" ); document.write( "

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