Let z = x+yi, where x and y are real and y < 0. Substitute this into w, simplify, and show that |w| > 1.
EDIT: Iíve just tried the problem, and I think a simpler method is to express z in terms of w and let w = u+vi instead. After substituting and simplifying, you should get
Since Im(z) < 0, the rest is straightforward.
EDIT again: For the second part of the questionset Im(z) = 0.How will w move as z travels along the real axis from -infinity to +infinity.