Answer:
B) - 1.
Step-by-step explanation:
Given : [tex]i^{58}[/tex].
To find : Solve it.
Solution : We have given [tex]i^{58}[/tex].
We know that even power of imaginary number is -1 .
[tex]i^{2}[/tex] = -1.
So, [tex](i^{2})^{2}= 1[/tex].
[tex](i^{4})= 1[/tex].
We can write [tex]i^{58}[/tex] as [tex](i^{4})^{14}[/tex].
Then [tex]i^{58}[/tex]= [tex](i^{4})^{14}[/tex] * [tex]i^{2}[/tex].
Plug [tex](i^{4})= 1[/tex] and [tex]i^{2}[/tex] = -1.
[tex]i^{58}[/tex]= [tex](1^{14})[/tex] * [tex]i^{2}[/tex]
[tex]i^{58}[/tex] = 1 *-1.
[tex]i^{58}[/tex] = -1.
Therefore, B) - 1.
