1) The square S in z plane has vertices at (0,0), (1,0), (1,1), (0,1). Find region in w plane into which S is mapped under transformations:
i) w=z^{2^{}}
ii) w=1/(z+1))
2) Consider w^{3}=z and assume that corresponding to z=1, we have w=1. i) if we begin at z=1 in z plane and make 1 complete circuit counterlockwise around origin, determine value of w on returning to z=1 for frist time. ii) find values of w on returning to z=1 after 2,3,4,... complete circuits about origin? Describe(i) and (ii) if paths do not enclose origin.