Q: Show w = z² is conformal except at 0. What does it do to the first quadrant? f'(z) = 2z ≠ 0 (z≠0): CONFORMAL (angles preserved!)! At 0: f' = 0: angles DOUBLE (not conformal!). First quadrant (0<θ<π/2): w: 0<arg<π: UPPER HALF-PLANE! (Squaring unfolds the quadrant!)