SOLUTION: how do you calculate high powers of "i" the imaginary number?

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Question 121923: how do you calculate high powers of "i" the imaginary number?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
how do you calculate high powers of "i" the imaginary number?
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Since i^4 = 1 divide your power by 4 and raise i to the power of the remainder.
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Example:
i^34 = i^(8*4+2) = i^2 = -1
i^117= i^(29*4+1)= i^1 = i
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Cheers,
Stan H.

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
The results of raising i to a power repeats in a pattern of 4 steps:
i%5E0=1, just like anything else to the 0 power
i%5E1=i
i%5E2=-1
i%5E3=%28-1%29%28i%29=-i
i%5E4=%28-1%29%28-1%29=1=i%5E0
i%5E5=i%5E4%2Ai%5E1=1%2Ai=i=i%5E1
i%5E6=i%5E4%2Ai%5E2=1%2A-1=-1=i%5E2
i%5E7=i%5E4%2Ai%5E3=1%2A%28-1%29%28i%29=-i=i%5E3
i%5E4=i%5E4%2Ai%5E4=1%2A%28-1%29%28-1%29=1=i%5E0
and so on...

So i%5En=i%5E%28n%2Amod4%29 where mod is the modulo function. a mod p returns the remainder when a is divided by p. In other words, take the exponent on i and integer divide by 4, look up the remainder in the first 4 elements of the table above, and that will be your answer.