SOLUTION: The imaginary number i is defined such that i^2 = �1. What does i + i^2 + i^3 + .... + i^23 equal? The answer is supposed to be -1, but I thought it should be -i according to anoth

Question 176697: The imaginary number i is defined such that i^2 = �1. What does i + i^2 + i^3 + .... + i^23 equal? The answer is supposed to be -1, but I thought it should be -i according to another source. Is the answer key wrong?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

, and so on repeating the sequence every 4 increments of the exponent.

The sum of the first 4 is: , so the sum of the each subsequent 4 must also be zero.

Use integer division is 5 with a remainder of 3. So in your string of 23 terms there are 5 sets of 4 terms each of which sum to zero, so it is only the last three terms that make any difference:

And that is your sum. It is your 'other source' that is incorrect.
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