Question

what is the value of $i^n$ if the remainder of $\frac{n}{4}$ is 2?
a. -1
b. -i
c. i
d. 1

Explanation:

Step1: Define n using remainder

If $\frac{n}{4}$ has remainder 2, then $n = 4k + 2$ for integer $k$.

Step2: Substitute n into $i^n$

$i^n = i^{4k+2} = (i^4)^k \cdot i^2$

Step3: Simplify using $i^4=1$, $i^2=-1$

$(1)^k \cdot (-1) = -1$

Answer:

A. -1