Solve for z, and give your answer in the form a+bi.
$$\overline{z+2-2i} = {2z + 5 - 7i}$$
I know fully understand the concept of complex numbers and complex conjugates. I've found that the answer is
$$ z = -3+3i $$
I don't know any proper methods to find the answer though, since I found this answer largely by trial and error. Any suggestions?
$\endgroup$ 41 Answer
$\begingroup$The given equation is equivalent to
$$\overline z=2z+3-9i\implies z=2\overline z+3+9i=2(2z+3-9i)+3+9i=4z+9-9i$$ so we solve for $z$ we find
$$z=-3+3i$$
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