Can someone help with the attached pic. Thanks
3 z z' + 2(z-z') =39 +12 j
where z' denotes the complex conjugate of z.
i. z z' = |z|^2
ii. z-z' = 2 j Im(z)
Hence we have |z|^2 = 39, and 2 Im(z) =12. Now write z=a+jb, then
a^2+b^2 = 39, and b=6,
a^2 = 3,
So all z satisfying the given equation are (sqrt(3) + 6j) and (-sqrt(3) + 6j).