Find all z satisfying:

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,

so:

a^2 = 3,

hence a=+/-sqrt(3)

So all z satisfying the given equation are (sqrt(3) + 6j) and (-sqrt(3) + 6j).

RonL