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Obtain the harmonic conjugate v of the function u=2x(1-y)
Obtain the Taylor series expansion of cos^2zabout z = 0.
b) Using the method of residues, evaluate the following integral:
∫0 to 2π{dθ/](3+2cosθ)}
Locate and name the singularities of the following functions in the finite z-plane:
1. ln(z+3i)/z^2

2. z^2-2z/(z^2+2z+2)
For the operator A=ax+ibp where a and b are constants, calculate [A,x] and [A,A]
For the operator A=ax+ibp where a and b are constants, calculate [A,x] and [A,A].
If f1(z) and f2(z) are two entire functions of order r1 and r2 respectively ,then show that (i) order of f1(z) - f2(z) <= max{r1, r2 } (ii) f1(z) . f2(z) <= max{r1 , r2}
Obtain the harmonic conjugate v of the function u=2x(1-y)
Obtain the Taylor series expansion of cos²z about z = 0.
Using the method of residues, evaluate the following integral:

∫ dθ/3+2cos(θ)
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