4. Squaring the complex plane = a) Let w = f(z) = 22, where z = x+iy and w=u+ iv. Sketch a contour map showing the curves in the z-plane that go to the lines u = 0, 1, 2, 3, 4 and v = 0, 1, 2, 3, 4 in the w- plane. Code the diagram (for example, with colors) so that the correspondence is easy to see. b) For w= f(z) = 22, sketch the curves in the w-plane that are the images of the lines x = 0, 1, 2, 3 and y = 0, 1, 2, 3 in the z-plane. Make the correspondence easy to see. 5. The exponential map Let w = f(z) =e, where z = x+iy and wu + iv. Sketch each region in the z-plane and its image in the w-plane under the transformation f. a) The vertical strip 0≤x≤1 b) The half plane x < 0 c) The rectangle 1≤x≤2, π/4≤ y ≤3π/4