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# Evaluate the following integrals22_22$dz (2+1)2(22+4)cis the circle Iz| = 5[9]4-32$ (Z(2-1)(2-2) dz _ cis the circle Iz/ = 3[6]Find the harmonic conjugate function...

## Question

###### Evaluate the following integrals22_22$dz (2+1)2(22+4)cis the circle Iz| = 5[9]4-32$ (Z(2-1)(2-2) dz _ cis the circle Iz/ = 3[6]Find the harmonic conjugate function of u = e-3xcos(3y). Hence show that analytic function f(z) = e-3z + ik where k is a constant [10]

Evaluate the following integrals 22_22 $dz (2+1)2(22+4) cis the circle Iz| = 5 [9] 4-32$ (Z(2-1)(2-2) dz _ cis the circle Iz/ = 3 [6] Find the harmonic conjugate function of u = e-3xcos(3y). Hence show that analytic function f(z) = e-3z + ik where k is a constant [10]

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