SOLUTION: hi, need help with simplifying complex number i^51, have no idea how to do it, if you can explain it please i will appreciate it

SOLUTION: hi, need help with simplifying complex number i^51, have no idea how to do it, if you can explain it please i will appreciate it

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Question 33940: hi, need help with simplifying complex number
i^51, have no idea how to do it, if you can explain it please i will appreciate it
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
powers of "i" go thru a cycle; i, i^2=-1, i^3=-i, i^4=1
So, divide 51 by 4 to get 12 with a remainder of 3
Then i^51=[(i^4)^(12)](i^3)= [(1^12)][-i]= -i
Cheers,
Stan H.
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