1998 AIME Problem 13

If \{a_1,a_2,a_3,\ldots,a_n\} is a set of real numbers, indexed so that a_1 < a_2 < a_3 < \cdots < a_n, its *complex power sum* is defined to be a_1i + a_2i^2+ a_3i^3 + \cdots + a_ni^n, where i^2 = - 1. Let S_n be the sum of the complex power sums of all nonempty subsets of \{1,2,\ldots,n\}. Given that S_8 = - 176 - 64i and S_9 = p + qi, where p and q are integers, find \left\lvert p\right\rvert + \left\lvert q\right\rvert.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.