document.write( "Question 295781: Please could you help me solve this equation: Find a complex number (z=x+iy)which satisfies the equation $\"2z%2Biz=2\"$ (the second z has a conjugate sign above it) \n" ); document.write( "

Algebra.Com's Answer #213210 by Fombitz(32388) $\"\"$ $\"About$

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$\"2%28x%2Biy%29%2Bi%28x-iy%29=2\"$
\n" ); document.write( " $\"2x%2B2yi%2Bxi-i%5E2y=2\"$
\n" ); document.write( " $\"%282x%2By%29%2B%28x%2B2y%29i=2%2B0i\"$
\n" ); document.write( "So then solving for both the real and imaginary part leads to two equations,
\n" ); document.write( "1. $\"2x%2By=2\"$
\n" ); document.write( "2. $\"x%2B2y=0\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"x%2B2y=0\"$
\n" ); document.write( " $\"x=-2y\"$
\n" ); document.write( " $\"2x=-4y\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"-4y%2By=2\"$
\n" ); document.write( " $\"-3y=2\"$
\n" ); document.write( " $\"highlight%28+y=-2%2F3%29%29\"$
\n" ); document.write( "Then from eq. 1,
\n" ); document.write( " $\"x=-2y\"$
\n" ); document.write( " $\"x=-2%28-2%2F3%29\"$
\n" ); document.write( " $\"highlight%28+x=4%2F3%29\"$
\n" ); document.write( " $\"z=%284%2F3%29-%282%2F3%29i\"$ \n" ); document.write( "

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