Answer:
i
Step-by-step explanation:
[tex]\begin{array}{lclcr}i^{1} & = &(\sqrt{-1})^{1}&=& i\\i^{2} & = & (\sqrt{-1})^{2}& =&-1\\i^{3} & = & (\sqrt{-1})^{3}&=&-i\\i^{4} & = & (\sqrt{-1})^{4}& = &1\\\end{array}[/tex]
Multiplying by i repeats the pattern
.
Thus, any i⁴ⁿ = 1
If n = 3, 4n = 12, so
i¹² = 1 and
i¹³ = i¹ = i
