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2. Let f be the branch of z1/4 such that z]> 0 and 0 < argz < 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 < argz < 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 < argz < 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(z) 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 [ f(z) dz?