Describe sets and images under the given function

Question

Sketch and describe the following sets and their images under the function z → z².

(a) The set of all points of the form z = x + 2i.

(b) The set of all points of the form z = x + 2xi.

(c) The set of all points on the upper half of the unit circle centred at the origin, that is, points z with polar coordinates (r, ?) such that r = 1 and 0.