I've been struggling with figuring out how to add powers of $i$.
For example, the result of $i^3 + i^4 + i^5$ is $1$. But how do I get the result of $i^3 + i^4 + ... + i^{50}$? Writing it all down would be pretty mundane...
It has to do something with division by 4, since the "power cycle" of $i$ repeats every fourth power.
Thank you for any clues.