Show that the Riemann surface of w = √(z - 1)(z - 2) has branch points at 1 and 2 sheets, which we may cut and join crosswise from 1 to 2. Introduce polar coordinates z - 1 = r₁e^iθ1 and z - 2 = r₂e^iθ2, so that w = √r₁r₂e^{i(θ1+ θ2)/2}.