## anonymous 5 years ago Evaluate i^26

1. anonymous

-1*4^(-13i)

2. anonymous

The book is saying -1?

3. anonymous

Maybe 1?

4. anonymous

sorry i'm not good with imaginary numbers. i just plugged it in the calculator and that's what i got.

5. anonymous

Yeah I'm not either. That's why I am here. Thanks anyway!

6. myininaya

26/4=6+remaider 2 i^2=-1

7. amistre64

8. myininaya

divide by 4 i^[4*6+2]=1^6i^2=1*(-1)=-1

The best way to do this is to think about `sections' of i. We know the following four things: \begin{align} i^2 &= \sqrt{-1}^2 = -1\\ i^3 &= i^2 \cdot i = -1 \cdot i = -i\\ i^4 &= i^2 \cdot i^2 = -1 \cdot -1 = 1 \end{align} From that, we can derive any power of i. That's what myininaya has done.

I said 4 --> I meant the following 3 things :) The fourth is that i is just i.

11. anonymous

I was coming up with( i^4)^5 *i^6

12. anonymous

Then i^5-i^6=1?

Well, that's close. Note that $$i^6$$ is actually $$i^{4 + 2}$$, so it's really $$(i^4)^6 \cdot i^2$$.

14. amistre64

And since i^4 is always 1, 1^6 is always 1, you are left only with $$i^2$$, which is -1.

16. amistre64

26/4 = 8. R2 i^2 = -1

17. anonymous

Got it! Thanks for your help!

18. myininaya

haha amistre your quotient is wrong

19. amistre64

lol.... I had a quotient ?

20. myininaya

26/4=6. R2

21. amistre64

LOL... yeah it is. but its so hard to remember all this stuff from kindergarten ;)

22. myininaya

lol

23. anonymous

Ouch you guys are killing me. This is actually Int Algebra - College.