Show that the bilinear mapping
where θ0 is a real constant 0 ≤ θ0 2π, z0 a fixed complex number and z*0 its conjugate, maps the upper half of the z plane (Im(z) > 0) onto the inside of the unit circle in the w plane (|w| 1). Find the values of z0 and θ0 if w = 0 corresponds to z = ∞.