Statistics Question

Math 3XX3 2024 (Winter) Assignment 3 Due Date: March 11, 2024 at 11:50 pm Instructions: Upload your scanned answers into the appropriate box for each question in Crowdmark. Question 1. [3 marks] Evaluate the integral Z 2 zez dz C where C is the part of the parabola y = x2 from z = 0 to z = 1 + i. Do not do it by brute force. Use the theorem in section 48 of [BC]. Question 2. [8 marks] For each of the curves listed below, evaluate the integral Z ez dz. 2 C z (z − iπ) (i) C is the circle |z − iπ| = 1. (ii) C is the circle |z| = 1. 1 (iii) C is the circle |z| = 5. (Do a partial fraction decomposition for z 2 (z−iπ) .) Question 3. [4 marks] Use the Cauchy integral formula for higher derivatives (the theorem in section 55 of [BC] or p. 70 of lecture notes Feb. 29) to evaluate the integral n Z z dz z−1 |z−1|=1 1