## starrhunter 3 years ago rationalize the denominator of √-16 _________ (1+i)+(6+3i)

1. m_charron2

-16 can be written as the product of 16 and -1, right? so what's the sqrt of 16 and the sqrt of -1?

2. starrhunter

i haven't any idea

3. hashsam1

|dw:1337100713360:dw|

4. m_charron2

ok, sqrt of 16, what multiplied with itself gives 16?

5. starrhunter

4

6. m_charron2

7. starrhunter

im not sure about the -1

8. starrhunter

there isnt an answer for that... right?

9. hashsam1

|dw:1337100894030:dw|

10. m_charron2

ok, I'll give you that one, because it's a bit tricky, it's actually i. i * i = -1

11. starrhunter

i times i. got it.

12. m_charron2

ok, perfect, so sqrt of -16 = sqrt 16 * sqrt -1 = 4 * i

13. starrhunter

but its negative 16 under the square root....

14. starrhunter

and none of that is one of my choices

15. starrhunter

all of my choices look like fractions

16. m_charron2

Yup, and it's still works because of this : $\sqrt{xy} = \sqrt{x} * \sqrt{y}$ right, so once you solve the the denominator, go back to hashsam1's solution

17. hashsam1

|dw:1337101077852:dw|

18. starrhunter

so it would be

19. hashsam1

|dw:1337101138650:dw|

20. starrhunter

thank you so much for all of your help!

21. hashsam1

22. hashsam1

23. starrhunter

its 16 + 28i over 65

24. m_charron2

perfect

25. starrhunter

|dw:1337101312782:dw|

26. starrhunter

yay!

27. hashsam1

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