Please assist me with the power of i(imaginary)

Let's raise i to various powers starting with 0,1,2,3...

i^0 = 1

i^1 = i

i^2 = ( sqrt(-1) )^2 = -1

i^3 = i^2*i = -1*i = -i

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

i^5 = i^4*i = 1*i = i

i^6 = i^5*i = i*i = i^2 = -1

We see that the pattern repeats itself after 4 iterations. The four items to memorize are

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.

To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.

This means i^25 = i^1 = i

Likewise,

i^5689 = i^1 = i

because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !