## anonymous 4 years ago rationalize the denominator of √-16 _________ (1+i)+(6+3i)

1. anonymous

-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. anonymous

i haven't any idea

3. anonymous

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4. anonymous

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

5. anonymous

4

6. anonymous

7. anonymous

im not sure about the -1

8. anonymous

there isnt an answer for that... right?

9. anonymous

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10. anonymous

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

11. anonymous

i times i. got it.

12. anonymous

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

13. anonymous

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

14. anonymous

and none of that is one of my choices

15. anonymous

all of my choices look like fractions

16. anonymous

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. anonymous

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18. anonymous

so it would be

19. anonymous

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20. anonymous

thank you so much for all of your help!

21. anonymous

22. anonymous

23. anonymous

its 16 + 28i over 65

24. anonymous

perfect

25. anonymous

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26. anonymous

yay!

27. anonymous

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