## gfields444 3 years ago How would i rationalize 6/ 3+i

1. Outkast3r09

multiply by the conjugate

2. Outkast3r09

multiply by 1 using the conjugate*

3. estudier

* top n bottom by 3-i

4. gfields444

So 9i?

5. estudier

6(3-i) / (3+i)(3-i)

6. gfields444

Is that all that I have to do? I'm not really sure how to do these sorts of problems

7. estudier

You need to multiply out the brackets and simplify if possible

8. estudier

Just like normal except you have i's to deal with...

9. gfields444

6(3-i)? Wouldn't the bottom cancel itself out?

10. estudier

It is a kind of trick to get rid of the i on the bottom.....

11. estudier

Similar to how you get rid of a rdical, same sort of idea...

12. gfields444

So confused

13. estudier

Multiply it out and you will see...

14. gfields444

9-i/9

15. gfields444

which you could divide 9 by 9 to get one, so -i?

16. estudier

6(3-i) is 18-6i Where do you get 9-i from?

17. gfields444

Oh wow opps. haha I added.

18. estudier

Ok, now what do you get for the bottom?

19. gfields444

9?

20. estudier

You have (3+i)(3-i) Tell me how it comes to 9

21. gfields444

You multiply and the +i and -i cancel out? i'm really sorry, this is new to me haha

22. estudier

(3+i)(3-i) is 3*3 + 3*i -3*i - i^2 (using FOIL?)

23. estudier

So the 3i's cancel out and leave 9-i^2 So what is i^2 ?

24. gfields444

-1

25. estudier

Right, so what is the bottom ( hint-it is not 9)

26. gfields444

8?

27. estudier

9-(-1)

28. gfields444

10

29. estudier

Ok so finally you have 18-6i/10 which you can divide by 2 to get 9-3i/5 as a final answer.

30. estudier

So, procedure for these is *by conjugate top and bottom then simplify

31. gfields444

thank you so much!!!

32. estudier

ur welcome