document.write( "Question 216176: Hi, I was wondering if someone could help me with this problem.\r
\n" ); document.write( "\n" ); document.write( "Simplify the following by hand. Give the answer in the form a+bi (a, b are real).\r
\n" ); document.write( "\n" ); document.write( "(2-i)/(5+i)\r
\n" ); document.write( "\n" ); document.write( "Thanks, Judy \n" ); document.write( "

Algebra.Com's Answer #163323 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Simplify the following by hand. Give the answer in the form a+bi (a, b are real).
\n" ); document.write( " $\"%28%282-i%29%29%2F%28%285%2Bi%29%29\"$
\n" ); document.write( "Multiply the equation by the conjugate of the denominator over itself
\n" ); document.write( " $\"%28%282-i%29%29%2F%28%285%2Bi%29%29\"$ * $\"%28%285-i%29%29%2F%28%285-i%29%29\"$
\n" ); document.write( "FOIL and combine like terms
\n" ); document.write( " $\"%2810+-+2i+-+5i+%2B+i%5E2%29%2F%2825+-+5i+%2B+5i+%2B+i%5E2%29\"$ = $\"%2810+-+7i+%2B+i%5E2%29%2F%2825+-+i%5E2%29\"$
\n" ); document.write( "remember i^2 = -1
\n" ); document.write( " $\"%2810+-+7i+%2B+%28-1%29%29%2F%2825+-+%28-1%29%29\"$ = $\"%2810+-+7i+-+1%29%2F%2825+%2B+1%29\"$ = $\"%289+-+7i%29%2F26\"$ 0r $\"9%2F26\"$ - $\"%287i%29%2F26\"$ \n" ); document.write( "

\n" );