Answer:
[tex]i^{85} = i[/tex]
Step-by-step explanation:
The options are missing; however, the question can still be solved.
Given
[tex]Number = i^{85}[/tex]
Required
Simplify
[tex]Number = i^{85}[/tex]
Rewrite 85 as 84 + 1
[tex]Number = i^{84 + 1}[/tex]
Split the expression using the law of indices
[tex]Number = i^{84} * i^1[/tex]
Rewrite 84 as 4(21)
[tex]Number = (i^{4})^{21} * i^1[/tex]
In complex numbers, [tex]i^4 = 1[/tex]
So, we have
[tex]Number = 1^{21} * i^1[/tex]
[tex]Number = 1 * i[/tex]
[tex]Number = i[/tex]
Hence;
[tex]i^{85} = i[/tex]
