AMC 12 2010b 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 $\{i^x, (1+i)^y, z\}$, where $i=\sqrt{-1}$?

\textbf{(A)}\ 149 \textbf{(B)}\ 205 \textbf{(C)}\ 215 \textbf{(D)}\ 225 \textbf{(E)}\ 235