1. The problem statement, all variables and given/known data (a) Use the polar form of the Cauchy-Riemann equations to show that: g(z) = ln(r) + i(theta); r > 0 and 0 < (theta) < 2pi is analytic in the given region and find its derivative. (b) then show that the composite function G(z) = g(z^2 + 1) is analytic in the quadrant x > 0 and y > 0 and find its derivative. 3. The attempt at a solution Ive done part (a) and got the correct answer, but I am having some trouble with (b). The main question I have is, how do I write this composite function? I can write: z^2 + 1 as r^2(cos(2(theta)) + 1) + ir^2(sin(2(theta))) but I dont know if that helps me. Thank you for your help!