Answer:
D
Step-by-step explanation:
So, recall the four basic i exponents:
[tex]i^1=i\\i^2=-1\\i^3=-i\\i^4=i[/tex]
The strategy here is to write the expression in terms of i to the fourth times another i.
For instance, 39 is the same as 36 plus 3. In other words:
[tex]i^{39}=i^{36}\cdot i^3[/tex]
Now, i^36 is the same as (i^4)^9. So:
[tex]i^{39}=(i^{4})^9\cdot i^3[/tex]
And as we already know, i to the fourth is 1. So:
[tex]i^{39}=(1)^9\cdot i^3[/tex]
Simplify:
[tex]i^{39}=i^3[/tex]
Again, i to the third is -i. So:
[tex]i^{39}=-i[/tex]
Our answer is D.
And we're done!
