Let z denote any nonzero complex number, written z = rele (- < 0 ), and let ra denote any fixed positive integer (n = 1, 2,...). Show that all of the values of log(z/") are given by the equation log(z/") == In n 100 ELEMENTARY FUNCTIONS Inr+i 11 +2(pn+k) n where p = 0, 1, 2, ... and k = 0, 1, 2,..., n-1. Then, after writing 1 0 +29 log z = Inr+i n n CHAP. 3 where q = 0, 1, +2, ..., show that the set of values of log(z/") is the same as the set of values of (1/n) log z. Thus show that log(z/") = (1/n) log z where, corresponding to a value of log(z/") taken on the left, the appropriate value of log z is to be selected on the right, and conversely. [The result in Exercise 5, Sec. 33, is a special case of this one.] - Suggestion: Use the fact that the remainder upon dividing an integer by a positive integer n is always an integer between 0 and n 1, inclusive; that is, when a positive integer n is specified, any integer q can be written q = and k has one of the values k = 0, 1, 2,..., n - 1. pn + k, where p is an integer