SOLUTION: can you please explain the answer to i^49? I factor out 13*3, but cannot resolve the remaining terms...thanks

Question 172894: can you please explain the answer to i^49? I factor out 13*3, but cannot resolve the remaining terms...thanks
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
can you please explain the answer to i^49? I factor out 13*3, but cannot resolve the remaining terms...thanks
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That's not clear. 13*3 = 39. What does that have to do with anything?
Is i = sqrt(-1)? Or is it just a variable?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Take note that 49 = 48 + 1 and 48 = 12*4.

Also, we'll use the identities and

So

This means that

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If you want an easier method, do the following:

Divide the exponent 49 by 4 to get 12 remainder 1

Since the remainder is 1, this tells us that the answer is "i" (ie )

This is a handy thing to remember (or put in your reference book)

If the remainder is 0, the answer is 1
If the remainder is 1, the answer is "i"
If the remainder is 2, the answer is -1
If the remainder is 3, the answer is "-i"
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