Question

Simplify the question With Steps

i^50 (It is iota with 50. as an exponent)

Answer 1

steps. convert it to a positive exponent
then evaluate the exponent
then flip the fraction

Answer 2

There's no way to begin until we know the value of ' i ' .

If ' i ' doesn't represent √-1 , then we can stop here
and discard the question as unanswerable.

If ' i ' is the famous √-1 , then here's how i⁵⁰ can be simplified:

Notice the following:
-- The 1st power of i is √-1 .
-- The 2nd power of i is (√-1)² = -1
-- The 3rd power of i is -√-1
-- The 4th power of i is (-√-1)·(√-1) = -(-1) = 1 .
-- Every 4 powers of ' i ' brings you back to ' 1 '.

So from the exponent of 50, you can knock out
the largest possible multiple of 4 , and evaluate
what's left.

50 = 48 + 2

i⁵⁰ = i² = -1 .