1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]
2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]
which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]
