document.write( "Question 432413: how do you find real numbers x and y for which (x+2i)(y-i)=-4-7i \n" ); document.write( "

Algebra.Com's Answer #299829 by Gogonati(855) $\"\"$ $\"About$

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To find the real numbers x and y, we first expand the left side of equality:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2Ay-x%2Ai%2B2y%2Ai-2%2Ai%5E2=-4-7i\"$ , simplify\r
\n" ); document.write( "\n" ); document.write( " $\"x%2Ay-%28x-2y%29%2Ai%2B2=-4-7i\"$ , (as you know i^2=-1)\r
\n" ); document.write( "\n" ); document.write( " $\"x%2Ay%2B2-%28x-2y%29%2Ai=-4-7i\"$ , As we know two complex numbers are equal if and only if their real parts and imaginary parts are equal.Thus, we write:\r
\n" ); document.write( "\n" ); document.write( " $\"system%28x%2Ay%2B2=-4%2C+x-2y=7%29\"$ , rewrite the system\r
\n" ); document.write( "\n" ); document.write( " $\"system%28%287%2B2y%29%2Ay=-6%2C+x=7%2B2y%29\"$ , solve the first equation\r
\n" ); document.write( "\n" ); document.write( " $\"2y%5E2%2B7y%2B6=0\"$ and find y=-2 and y=-3/2 Substitute and find values of x\r
\n" ); document.write( "\n" ); document.write( " x=7+2*(-2)=3 and x=7+2*(-3/2)=4, thus, we have two solution, there are:\r
\n" ); document.write( "\n" ); document.write( "((3,-2) and (4, -3/2). \r
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