is there a way to plot a complex relation?

[Cygnus]

im trying to plot this relation:

Re(−3 + 3 i + conj(z) ) = Im(−4 + 4 i + conj(z) )

z = x+y*i

i've been searching for hours how to plot this so as my last resort I came to this forum.

[Albert Chan]

XCas 1.4.9-57(win32): config = exact real RAD 12 XCas

z := x + y*i
solve(re(-3 + 3*i + conj(z)) = im(-4 + 4*i + conj(z)), y) ==> [-x + 7]
plot(-x + 7)