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2. Let f be the branch of z¹/4 such that z> 0 and 0 < arg z < 2. Let C denote the semi-circular path z=2e¹0 (0 ≤0 ≤ π).
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2. Let f be the branch of z¹/4 such that z> 0 and 0 < arg z < 2. Let C denote the semi-circular path z=2e¹0 (0 ≤0 ≤ π).
2. Let f be the branch of z¹/4 such that z> 0 and 0 < arg z < 2. Let C denote the semi-circular path z=2e¹0 (0 ≤0 ≤ π). (a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z'(0) exist and calculate their values. (b) Calculate [ f(2) dz. (c) Why did we show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z' (0) exist before calculating Jo f(z) dz?