 |
| ||
| |||
|
| Math Central | Quandaries & 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!
RD
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.