Answer:
[tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.
Step-by-step explanation:
Since i = [tex]\sqrt{(-1)}[/tex]
i² = (-1)
[tex]i^{3}=-i[/tex]
[tex]i^{4}=(-1)^{2}[/tex] = 1
[tex]i^{8}=1^{2}[/tex] = 1
[tex](i^{8})^{2}=1[/tex]
[tex]i^{34}=[i^{17}]^2[/tex]
= [tex](i^{8}\times i^{8}\times i)^{2}[/tex]
= [1 × 1 × √(-1)]²
= 1² × 1² × [√(-1)]²
= (-1)
Therefore, [tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.
