Question

How do you simplify i^256? What is i^256 simplified?

A) Divide 256 by 8 and multiply the remainder times i; 0
B) Divide 256 by 4 and use the remainder of 0 as the new power of i.; 1
C) Divide 256 by 6 and use the remainder of 0 as the new power of i.; 0
D) Divide 256 by 6 and use the remainder of 0 as the new power of i.; -1

Answer 1

Explanation:

You have that
`i^2=-1`, so we must have

`i^4=(i^2 )(i^2)=(-1)(-1)=1`.

This says that we must make groups of four
`i`'s for simplify because they becomes 1, and the last group that is not of four
`i`'s is the result.

This is equivalent to divide 256 by 4 and use the remainder of that division, that is 0, as the new power of
`i`, and the result is 1 because
`i^0 =1.`. You can see the operation:

`i^(256) = (i^4)^(64)* i^0 =1`