If C is the positively oriented circle represented by |z| = 2, then the value of the contour integral ∮C e2zz4 dz 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?