1. Verify the CR equation for f(z)= |xy| at z= (0,0) and also discuss the differentiability and analyticity of the f(z). [xy + ixy6 x +0 2. Examine the nature of the function f(z) = 0, -, (x, y) = (0,0) (x, y) = (0,0) 1 3. Find the image of the unit circle under the transformation f(z) = z+, and also find critical points. 4. Find the image of the unit circle under the transformation, f(z) = Z Z - and also find 1 fixed points. 5. Find the bilinear transformation which maps the points 1,i,-1 onto the points 0,1,00 and show that this transformation maps the interior of the unit circle of the z-plane onto the upper half of the w-plane.