SOLUTION: Please could you help me solve this equation: Find a complex number (z=x+iy)which satisfies the equation {{{2z+iz=2}}}(the second z has a conjugate sign above it)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please could you help me solve this equation: Find a complex number (z=x+iy)which satisfies the equation {{{2z+iz=2}}}(the second z has a conjugate sign above it)      Log On


   

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)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x%2Biy%29%2Bi%28x-iy%29=2
2x%2B2yi%2Bxi-i%5E2y=2
%282x%2By%29%2B%28x%2B2y%29i=2%2B0i
So then solving for both the real and imaginary part leads to two equations,
1.2x%2By=2
2.x%2B2y=0
From eq. 2,
x%2B2y=0
x=-2y
2x=-4y
Substitute into eq. 1,
-4y%2By=2
-3y=2
highlight%28+y=-2%2F3%29%29
Then from eq. 1,
x=-2y
x=-2%28-2%2F3%29
highlight%28+x=4%2F3%29
z=%284%2F3%29-%282%2F3%29i