## Fools101 5 years ago Imaginary Numbers Simplify i 9

1. Fools101

2. pottersheep

That is simplified isnt it?

3. Fools101

oh also it i^9

4. pottersheep

ah. ok then so 1^2 = -1 right

5. anonymous

simplified version has to be i

6. Fools101

Aww idk this kind of confusing me

7. pottersheep

(i^2)^4 . i (-1)^4 . i 1i

8. pottersheep

(i^2)^4 . i (-1)^4 . i 1i

9. anonymous

any variable equals 1 automatically

10. pottersheep

Do you get it?

11. pottersheep

Basically take out an i^2 first so that you work with -1. I.e i^4 = (i^2)^2 so now you have (-1)^2 = 1. Do you understand up to there?

12. Fools101

KIND of so it 1? a little ...

13. anonymous

if there is no value to a variable it becomes a 1.

14. Fools101

then the i Crossout ?

15. myininaya

$i^9=i^{4 \cdot 2 +1}=i^{4 \cdot 2} \cdot i^1=(i^4)^2 \cdot i=(1)^2 \cdot i$ $=1 \cdot i=i$

16. anonymous

pattern is $i^0=1$ $i^1=i$ $i^2=-1$ $i^3=-i$ $i^4=1$ and so on. so your real job is to take the integer remainder when you divide the power by 4. for example $i^{103}=i^3=-i$

17. Fools101

ohhhh i see !!! kk thank u that make sense !!!

18. anonymous

yw