5Determine the location of the poles of the function 1cosz C

(5)Determine the location of the poles of the function 1/cos(z). Calculate the residue at the pole z= Pi/2.

Solution

1)

Possible poles appear when cosz =0

cosz =0

z = [(2n+1)pi]/2

So location of poles are (2n+1)pi/2 where n=0,1,2.......

2)

series expansion of cosz = 1 - z^2/2 + O(z^4)

so 1/(1 - z^2/2 + O(z^4))

So residule at z = pi/2 = 0

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