Question please answer!!!! !!!

Question

asked Sep 2, 2021 16.2k views

1 Answer

Kasongoyo · Answer 1 · 2021-09-06T23:37:49+0000

Answer:

D

Explanation:

So, recall the four basic i exponents:

$i^1=i\\i^2=-1\\i^3=-i\\i^4=i$

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:

$i^(39)=i^(36)\cdot i^3$

Now, i^36 is the same as (i^4)^9. So:

$i^(39)=(i^(4))^9\cdot i^3$

And as we already know, i to the fourth is 1. So:

$i^(39)=(1)^9\cdot i^3$

Simplify:

i^(39)=i^3

Again, i to the third is -i. So:

i^(39)=-i

Our answer is D.

And we're done!