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How do you simplify #i^100#?

Answer 1

Chloe Alexander

#i^100 = 1#

#i^100 = (i^2)^50 = (-1)^50 = ((-1)^2)^25 = 1^25 = 1#

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Answer 2

Sophie Adams

#1#

Even powers of #i# are equal to #1#

Odd powers of #i# are equal to plus or minus #i# The signs alternate

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Answer 3

Liam Brennan

To simplify (i^{100}):

Recognize that (i) represents the imaginary unit, where (i^2 = -1).
Since (i^2 = -1), (i^4 = (-1)(-1) = 1).
Every power of (i) that is a multiple of 4 will simplify to 1.
(100) is divisible by (4), so (i^{100}) simplifies to (1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.