Mathematics: Question please answer

Question please answer - id7440803, jojo171717

mooreadrian412

01.02.2022

Step-by-step 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!

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