SOLUTION: How do you simplify i^-33. I'm not sure how to deal with the negative exponent. Please help.

Question 179689: How do you simplify i^-33. I'm not sure how to deal with the negative exponent. Please help.
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, rewrite the expression to get rid of the negative exponent. Simply flip the fraction to get:

Now divide 33 into 4 to get 8 remainder 1

Since we get a remainder 1, this tells us that

So

Start with the given expression.

Multiply the fraction by

Combine the fractions

Multiply

Replace with -1 (since )

Reduce

So

or more simply
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!

:
=
:
1/i
:
multiply top and bottom by -i
:

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