Complex Analysis Answers

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]

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:
2π
∫ dθ/3+2cos(θ)
0

Locate and name the singularities of the following functions in the finite z-plane:
i) ln(z+3i)/z²
ii) (z²-2z)/(z²+2z+2)

simplify this complex number
cos3x + jsin3x / cosx + jsinx

Evaluate |3+4i|