Question

Given a positive integer n such that i^n = 1, which of the following statements about n must be true? (Note i^2 = -1)

F. When n is divided by 4, the remainder is 0.
G. When n is divided by 4, the remainder is 1.
H. When n is divided by 4, the remainder is 2.
J. When n is divided by 4, the remainder is 3.
K. Cannot be determined from the given information

Answer 1

F. When n is divided by 4, the remainder is 0. is true

Answer 2

Answer:

The correct option is F.

Step-by-step explanation:

Consider the provided information.

$i^n=1$

It is given that $i^2=-1$

By squaring both sides we get,

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

$i^4=1$

Now compare $i^4=1$ with the provided equation $i^n=1$.

By comparison, it can be concluded that n = 4.

Now, consider the provided option.

In each option, we need to divide n by 4 or we can say 4 divided by 4.

If we divide 4 with 4 it will give the remainder 0.

Therefore, the correct option is F.