Thank you for the opportunity to help you with your question!
i^1 = i i^2 = -1 i^3 = -i i^4 = 1
And it will keep going as i, -1, -i, 1, i, -1, -i, 1, etc. So any exponent that's a multiple of 4 will equal 1, and you can figure out the values of non-multiples by counting up or down from the multiple of 4.
So onto the your math problem! i = i i^2 = -1 i^3 = -i L = huh? i^23 = -i (i^24 is 1. One number before that in the pattern is -i).
I have no idea what the "L" means, so I will ignore it. If it's a typo, hopefully you will understand how to do it on your own. It will be pointless for me to continue, since the answer will be different from your choices. But....
i + i^2 + i^3 + i^23 = i - 1 - i - i = -i - 1
Just add whatever L is supposed to be. And there's your answer
Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 4th, 2015
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