Consider the function f(z): - 1 z(z+1) (a) Identify all the singular points. (4 marks) (b)...

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Consider the function f(z): - 1 z(z+1) (a) Identify all the singular points. (4 marks) (b) We are going to expand ƒ(z) about z = i. Sketch all the possible regions of convergence. (4 marks) (c) From (b), pick the region having the shape of a torus (2D donut). By making use of the following power series: (12 marks) 1 - Z Expand f(z) for this region. ∞ n=0 zn |z| < 1 Consider the function f(z): - 1 z(z+1) (a) Identify all the singular points. (4 marks) (b) We are going to expand ƒ(z) about z = i. Sketch all the possible regions of convergence. (4 marks) (c) From (b), pick the region having the shape of a torus (2D donut). By making use of the following power series: (12 marks) 1 - Z Expand f(z) for this region. ∞ n=0 zn |z| < 1