what is i plus i2 plus i3.....plus i23?

Mathematics
Tutor: None Selected Time limit: 1 Day

i dont understand the imaginary numbers stuff.

Jun 4th, 2015

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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