SOLUTION: Imaginary numbers i to the 37 power

Question 687981: Imaginary numbers
i to the 37 power
Found 3 solutions by jim_thompson5910, josh_jordan, lwsshak3:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
i^(37)

i^(36+1)

i^(36)*i^1

i^(36)*i

(i^(4*9))*i

(i^4)^9*i

(1)^9*i

1*i

i

So i^(37) = i
Answer by josh_jordan(263)   (Show Source): You can put this solution on YOUR website!
Take the power of i and divide by 4. In your case, i is raised to the 37th power. Divide 37 by 4, which is 9 with a remainder of 1. The remainder now goes above the i. So, i to the first power, is i.
So, = i
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Imaginary numbers
i to the 37 power
i=√-1
i^2=-1
i^3=-i
i^4=1
i^37=i^36*i=1*i=i
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