Solve this problem ( fundamentals of complex analysis with applications to engineering and science)

PlZ detail and clear.

1. Find the image of the line through 2 = 3 and w = 3i in the Riemann sphere. 2. Let f(z) : z/(z + 1) (a) determine the points where f(z) is continuous. (b) what point 2 maps to the point 2i under this function. (c) What is the image of the disk {2 | |zi f l}. 3. Determine in two ways where z) : e2 is differentiable. 4. (a) Let u be the function u(:::,y) : 12:92 dened in R2 \\ {(0,0)}. Show thatu is harmonic. (b) Find an analytic function f) on C \\ {0} of the form f = u. + in. 5. (a) Give an identity for 005(36) for real 6'. (b) Is this identity true for cos(32? (o) Is the identity sin2(z) + cos2 (2) : 1 true for ali z e C