## eroshea 3 years ago rationalize

1. eroshea

$\frac{ 4-4\sqrt{3}i }{ -2\sqrt{3}+2i }$

2. hartnn

multiply and divide by -2root3-2i

3. hartnn

or take -2i common from numerator. u get -2i(2i-2root 3) in numerator. so what gets cancelled?

4. eroshea

wait.. i'll try

5. eroshea

is there something that can be cancelled?

6. hartnn

see the factor in numerator and denominator!!

7. eroshea

owh.. -2i will remain??and the factor will cancel out the denominator?

8. hartnn

yup,-2i,got it ?

9. eroshea

but i think its wrong? i thnk this should be what in the numerator is , -2i(2i+2root3),, am i right??

10. hartnn

O.o

11. hartnn

options?

12. hartnn

and yes, u are right....

13. eroshea

i dont know what to do next

14. hartnn

multiply and divide by -2root3-2i

15. eroshea

i hate it when that "i" is in my solution .. :D i'll try solving it

16. eroshea

the denominator will be 8? but i have a difficulty in solving the numerator :((

17. hartnn

8 ?? or -16 ?

18. eroshea

my bad.. i believe the numerator should be 18?? 12-4i^2 = 12-4(-1) = 12+4= 16?

19. eroshea

i mean the DENOMINATOR

20. hartnn

*minus*

21. eroshea

y negative?

22. eroshea

$(-2\sqrt{3}+2i)(-2\sqrt{3}-2i) = (-2\sqrt{3})^{2}-4i ^{2}=12-4(-1)=16$

23. hartnn

my bad, sorry,i took - common from that....ok,so 16 numerator = ?

24. hartnn

and what are your options ?

25. eroshea

my final answer is -root3 - i

26. eroshea

if i simplified my numerator, -16root3 - 16i and divide that by 16 -root3 -i is my answer correct?

27. hartnn

hmm....its my silly mistake's day or i m getting i-root3

28. eroshea

owh @_@

29. eroshea

i'll try solving it again

30. eroshea

owh you're right!! hahaha... i had a mistake with my subtraction, 24i-8i should be 16i and not -16i.. thanks ! :))

31. hartnn

finally! welcome :)

32. eroshea

it's not your silly mistake day :))

33. hartnn

glad to know :)

34. eroshea

how long have you've been in this site?

35. hartnn

48 days around.....

36. eroshea

owh.. i just made my account yesterday :3 brb.. i'll just go out and eat first and then back in reviewing :)) i have my finals tomorrow for algebra and trigonometry

37. hartnn

best of luck.