Question

How do you simplify `i^247`?

Answer 1

A great trick to solving this type of problem is understanding that there are only 4 possible solution ...

Explanation:

Raising the imaginary number `i` to a power can only result in 4 possible solutions :

`i^0=1`
`i^1=i`
`i^2=-1`
`i^3=-i`

Here's the trick ... divide the exponent by the number 4 and calculate the remainder. Then, use the remainder as the new exponent .

In this example, `247/4=61 " with remainder " 3`

Answer: `i^247=i^3=-i`

hope that helped