4. Differential and analytic functions. Show that f(z) is differentiable for all zeC f(z)=e" cosx+ie sin x Where is the function f(z) = u+vi differentiable and/or analytic if u =2x3+24xy+1 v=12-2y-24 xy + 112 Where are the following functions differentiable/analytic: xi f(2)=zIm², ƒ(2)=1+1, f(z) = x² +iy² y 5. Moebius: Find the Moebius function that maps points (1,2i, 0) to (2, 0, 0) in that order. Find the Moebius function that maps circle centered at 1 with radius 2 to the circle centered at 1+i with radius 1. • Define cross-ratio and state its main property. • Find Mobius map that transform the unit circle onto itself and 0 to 1/2. (Beck 3.16, p. 63)