SOLUTION: simplify imaginary i^33 as much as possible

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Question 221204: simplify imaginary i^33
as much as possible
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
simplify imaginary i^33
as much as possible

Step 1. Since i=sqrt%28-1%29, then i%5E2=sqrt%5E2%28-1%29=-1. Also, i%5E3=-i and i%5E4=1

Step 2. Therefore i%5E33=%28i%5E4%29%5E8%2Ai=1%5E8%2Ai=i where %28i%5E4%29%5E8=i%5E32.

Step 3. ANSWER: i%5E33=i

I hope the above steps were helpful.

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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
simplify imaginary i^33 as much as possible

When calculating large powers of i, we simply need to divide the exponent by 4, and the remainder is our answer. That is:

i%5E33 = i%5E%2833%2F4%29 = i%5E8 and remainder of i%5E1. As mentioned before, this remainder i%5E1 will be the answer, which is highlight_green%28i%29