The mapping w = αz + β (a, β both constant complex numbers) maps the point z = 1 + j to the point w = j and the point z = -1 to the point w = 1 + j.
(a) Determine α and β.
(b) Find the region in the w plane corresponding to the upper half-plane Im(z) > 0 and illustrate diagrammatically.
(c) Find the region in the w plane corresponding to the disc |z| 2 and illustrate diagrammatically.
(d) Find the fixed point(s) of the mapping.
In (b)-(d) use the values of α and β determined in (a).