e3z (i) Find all the poles of the function f (z) = and plot them on...

 

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e3z (i) Find all the poles of the function f (z) = and plot them on 22(22 +22+2) (ii) an Argand diagram. Hence evaluate the integral of (2) dz, writing your solutions in the form a + jb where a and b are real, where (a) C is the circle ||=2 (b) C is the circle |z2| = 1. - (13 marks) By constructing a suitable contour in the complex plane, use the method of residues to evaluate the real integral I 1 = 1 1 1 1 dx X- e3z (i) Find all the poles of the function f (z) = and plot them on 22(22 +22+2) (ii) an Argand diagram. Hence evaluate the integral of (2) dz, writing your solutions in the form a + jb where a and b are real, where (a) C is the circle ||=2 (b) C is the circle |z2| = 1. - (13 marks) By constructing a suitable contour in the complex plane, use the method of residues to evaluate the real integral I 1 = 1 1 1 1 dx X-