The value of the integral ∫C 3z2 + zz2 - 1 dz, where C is the circle |z - 1| = 1, is:

Let h be a holomorphic function on ℂ ∖ {0} such that lim|z| → &infty; h(z) = 0. For every n ≥ 1, consider fn(z) = ∑k=1n h(zk). Let 𝔻 denote the open unit disc { z ∈ ℂ : |z| < 1 }. Which of the following statements is necessarily true?

Let γR(t) = 2 + i + R e2πi t for t ∈ [0, 1] and R = 1, 2. Which of the following statements is true?

Let S be a finite subset of ℂ containing 0. Let f : ℂ ∖ S → ℂ be a holomorphic function which has a simple pole at 0. For R > 0, let γR denote the path γR(t) = R e2πi t for t ∈ [0, 1]. Which of the following statements is necessarily true?

Let f be an analytic function on D = { z ∈ &mathbb;C : |z| < 2 } such that f is real-valued on the real axis segment (-2, 2). Then f(1 - i) is equal to:

Find the normal form of the bilinear transformation w = 3iz + 1z + i.

The radius of convergence of the power series ∑n=1∞ zn!n is:

What is the radius of convergence of the power series ∑n=0∞ znn!?

The fixed points of the bilinear transformation f(z) = 2iz + 5z - 2i are: