## anonymous one year ago Simplify i^16 A)-1 B)1 C)i D)-i

1. Astrophysics

Hint: $i^2 = -1$

2. anonymous

X it by 16?

3. Astrophysics

No, what if I write it as $i^{16} = i^2 \times i^2 \times i^2....$ 8 times

4. anonymous

$(i^2)^8 =~?$

5. Astrophysics

$(i^4)^4$

6. anonymous

1?

7. Astrophysics

Yup!

8. anonymous

$(i^2)^{32/4}$

9. anonymous

Lol ok im done.

10. Astrophysics

lol

11. anonymous

jhannybean don't know what you meant on that last comment you put lol

12. anonymous

Oh, i said im done trying to find derivations of the same thing : $$i^{16}$$ lol.

13. anonymous

I was talking about where you got 32/4

14. anonymous

any exponent of i divisible by 4=1 ie i^16, i^32, i^400 all = 1

15. anonymous

I would had never known that if you did not just tell me so thank you:)

16. anonymous

:)

17. Astrophysics

32/4 = 8