2. Let f be the branch of z ^1/4 such that |z| > 0 and 0 < arg z < 2π. Let C denote the semi-circular path z = 2e iθ (0

[answerhappygod]

2. Let f be the branch of z ^1/4 such that |z| > 0 and 0 <arg z < 2π. Let C denote the semi-circular path z = 2e iθ (0 ≤ θ≤ π). (a) Show that the right hand limits at θ = 0 of the real andimaginary parts of f[z(θ)]z ′ (θ) exist and calculate their values.(b) Calculate Z C f(z) dz.