Letz=x+yi, wherexandyare real andy< 0. Substitute this intow, simplify, and show that |w| > 1.

EDIT: I’ve just tried the problem, and I think a simpler method is to expresszin terms ofwand letw=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(How will w move as z travels along the real axis from -infinity to +infinity.z) = 0.