14.2 In the plane cut along (-,0], define the square root of z to be f(z)...

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14.2 In the plane cut along (-,0], define the square root of z to be f(z) = |2|1/2 e10/2 (0 z =|z|ei, <0). By using the identity (z + h) f(z) = h f(z+h) + f(z) prove that f'(2) exists and equals (z)/(2%) in C \ (,0]. By consid- ering d dz ( 1) . . ( n + 1) (4-(-1) n=0 n! (z 1)" for |z1| <1, obtain the Taylor expansion of in D(1; 1). 14.2 In the plane cut along (-,0], define the square root of z to be f(z) = |2|1/2 e10/2 (0 z =|z|ei, <0). By using the identity (z + h) f(z) = h f(z+h) + f(z) prove that f'(2) exists and equals (z)/(2%) in C \ (,0]. By consid- ering d dz ( 1) . . ( n + 1) (4-(-1) n=0 n! (z 1)" for |z1| <1, obtain the Taylor expansion of in D(1; 1).