(a) Let f: C C be differentiable at zo. Considering f as a map R?...

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(a) Let f: C → C be differentiable at zo. Considering f as a map R? → R?, that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotation matrix; that is, a matrix of the form prove cos(0) - sin(0) sin(0) cos(e) 1 where 0 E (-T, 7]. (b) If f = u + iv for functions u, v: R? → R, what are k and R in terms of u and v? (a) Let f: C → C be differentiable at zo. Considering f as a map R? → R?, that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotation matrix; that is, a matrix of the form prove cos(0) - sin(0) sin(0) cos(e) 1 where 0 E (-T, 7]. (b) If f = u + iv for functions u, v: R? → R, what are k and R in terms of u and v?

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