Question

What is the value of i^n if the remainder of n/4 is 2?A.-i B.1c. iD. -1

Answer 1

D. -1

Step-by-step explanation:

Given the quotient:

`(n)/(4)`

If the remainder of n/4 is 2, it means that the number n can be defined as follows:

`\begin{gathered} n=4x+2 \\ x\text{ the number of multiples of 4} \end{gathered}`

Clearly, the number n above is an even number.

When the complex number 'i' is raised to an even power, say 2, we have:

`\begin{gathered} i^2=(\sqrt[]{-1})^2 \\ =-1 \end{gathered}`

Therefore, the value of i^n if the remainder of n/4 is 2 is -1.