For the function f(z) = exp[z - 1 + 1/(z - 1)], the point z = 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?