3.1 Consider the following complex function: f(2)= (z + a)(z + b), where a > b>0 are real. Now: (a) State why f(z) is no

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3 1 Consider The Following Complex Function F 2 Z A Z B Where A B 0 Are Real Now A State Why F Z Is No 1 (53.25 KiB) Viewed 41 times

3.1 Consider the following complex function: f(2)= (z + a)(z + b), where a > b>0 are real. Now: (a) State why f(z) is not single-valued, [2] (b) find the branch points and isolated singularities of f(2), and state the nature of the isolated singularities, [4] (c) evaluate the residues of f(z) at its isolated singularities, assuming 0 < arg z < 2π, [6] (d) compute the integral fƒ(z)dz, where y is the contour in Fig. 1, and [4] (e) use the previous results to show that 2π ya - Vb dz √3 a-b [9] So (2x + a)(2x + b)² Z=