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  4. If K=4n+7 , then ik equals (n ∈ I)

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Q. If $K=4n+7$ , then $i^{k}$ equals $\left(n \in I\right)$

Complex Numbers and Quadratic Equations

Solution:

$i^{k}=i^{4n}\cdot i^{7}=\left(i^{4}\right)^{n} \left(i^{2}\right)^{3}i$
$=1\left(-1\right)\left(i\right)$
$=-i$