## Question

###### Considcr thc following paths: (i) a : [0, 2w] _ C, defined by a(t) = e2it _ (ii) 8 : [0, Vr] ~ â‚¬, defined by B(t) = 4+2e-2it?_ (iii) Y [0, 2w] , defined by -l+eit if t â‚¬ [0,T) , ~(t) 2 - 4i -4+4i + if t e [T, 2w].(a) Sketch cach of the paths above and check if it is a contour. Detcrminc whethcr cach contour has clockwise Or anticlockwise oricntation. (b) Computc thc length of cach path:

Considcr thc following paths: (i) a : [0, 2w] _ C, defined by a(t) = e2it _ (ii) 8 : [0, Vr] ~ â‚¬, defined by B(t) = 4+2e-2it?_ (iii) Y [0, 2w] , defined by -l+eit if t â‚¬ [0,T) , ~(t) 2 - 4i -4+4i + if t e [T, 2w]. (a) Sketch cach of the paths above and check if it is a contour. Detcrminc whethcr cach contour has clockwise Or anticlockwise oricntation. (b) Computc thc length of cach path:

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