SOLUTION: the subject area is on imaginary numbers. what is i to the power of 359 equal to.

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Question 176226: the subject area is on imaginary numbers. what is i to the power of 359 equal to.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
what is i to the power of 359 equal to.
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Recall that i^4 = 1
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359 = (4*89 + 3)
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i^359 = (i^4)^89 *i^3
= 1^89 * i^3
= i^3 = -i
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Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The powers of i go in a cycle of 4:

i%5E0+=+1

i%5E1+=+i

i%5E2+=+-1

i%5E3+=+i%5E2+%2A+i%5E1+=+-1+%2A+i+=+-i

i%5E4+=+i%5E2+%2A+i%5E2+=+-1+%2A+-1+=+1+=+i%5E0

and so on...

So, using integer division, divide 359 by 4 and find the remainder. i raised to the power of 359 is equal to i raised to the power of the remainder when 359 is divided by 4.