AMC 12B 2010 Problem 15

For how many ordered triples (x, y, z) of nonnegative integers less than 20 are there exactly two distinct elements in the set \left\{i^{x},(1+i)^{y}, z\right\}, where i=\sqrt{-1} ?

Answer Choices
A. 149
B. 205
C. 215
D. 225
E. 235