Consider the following algorithm: 1: Complex(n) 2: j = 1 3: a = 0 4: while j n 5: a = a + j 6: j = 2 j 7: end while (a) (20 pts) Using induction, prove that after the k-th iteration, a = 2k 1. (b) (10 pts) Compute the precise number of iterations that the while loop will execute. (c) (5 pts) Using your answers from parts (a) and (b), determine what Complex(n) returns and what the asymptotic running time of the algorithm is (use notation).