## Barrelracing one year ago Rationalize the denominator of square root of negative four over open parentheses 7 minus 3 i close parentheses plus open parentheses 2 plus 5 i.

1. Barrelracing

|dw:1437857496870:dw|

2. carolinar7

|dw:1437846970791:dw|

3. carolinar7

|dw:1437847013934:dw|

4. anonymous

|dw:1437846985513:dw|

5. carolinar7

No you need to multiply it by conjugate

6. carolinar7

7. anonymous

the first thing you have to do is combine the denominator into one complex number. |dw:1437847204733:dw|

8. anonymous

|dw:1437847105860:dw|

9. Barrelracing

5 - 2i

10. anonymous

that's (7 + 2) + (-3i + 5i)

11. Barrelracing

9 +2

12. anonymous

9 + 2i, so now you have $\frac{ \sqrt{-4} }{ 9+2i }$

13. anonymous

can you write √-4 in terms of i?

14. Barrelracing

no

15. anonymous

$\sqrt{-4}=\sqrt{4} \times \sqrt{-1}=2i$

16. anonymous

^do you understand that?

17. anonymous

so now we have $\frac{ 2i }{ 9+2i }$

18. anonymous

and now you can multiply by the conjugate like @carolinar7 said above

19. Barrelracing

ok I don't know how to do that

20. anonymous

to find the conjugate change the sign of the imaginary part of the denominator. → 9-2i Then multiply the numerator and denominator by it. $\frac{ 2i(9-2i) }{ (9+2i)(9-2i) }$ Distribute/foil and the i's will cancel in the denominator

21. Barrelracing

18i - 4/77

22. Barrelracing

-4+18i/77

23. anonymous

You had this at some point $\frac{ 18i-4i^2 }{ 81-4i^2 }$ Remember that i² = -1, so you'll have $\frac{ 4+18i }{ 85 }$

24. Barrelracing

thank you

25. anonymous

you're welcome