Conformal mapping for z^0.5

Hi, im trying to show that the conformal map for z^0.5 transforms the infinite plane to the half plane with x>=0. I have u + iv = (x + iy)^0.5 and Re^iφ = r^0.5 * e^iθ/2 (polar form). But i'm totally stuck on how to take it any further, I don't know how I can translate those equations into any graphs.