Math CentralQuandaries & Queries


Question from megan, a student:

how do you solve i+i^2+i^3+i^4...+i^102

Hi! You can't "solve" it - it's not an equation - but you can simplify it, by "putting it into closed form".

If you multiply it by $(1-i)$ almost every term in the product cancels; thus it is equal to $\large \frac{i-i^{103}}{1-i}$ (check the details; this is a trick that is useful to know.)

Good Hunting!

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