Question

How do you simplify `i^42`?

Answer 1

The imaginary number `i` can only take on 4 values when raised by a positive integer exponent.

Explanation:

`i^1=i`
`i^2=-1`
`i^3= -i`
`i^4=1`

Then, it simply cycles through the same values all over.

To find `i^42` just divide the exponent by 4 and find the remainder :

`42/4 = 10` with a remainder of 2. So, the value 2 is the exponent.

Answer: `i^2=-1`

Hope that helped