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starrhunter

  • 2 years ago

rationalize the denominator of √-16 _________ (1+i)+(6+3i)

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  1. m_charron2
    • 2 years ago
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    -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
    • 2 years ago
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    i haven't any idea

  3. hashsam1
    • 2 years ago
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    |dw:1337100713360:dw|

  4. m_charron2
    • 2 years ago
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    ok, sqrt of 16, what multiplied with itself gives 16?

  5. starrhunter
    • 2 years ago
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    4

  6. m_charron2
    • 2 years ago
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    ok, what about -1?

  7. starrhunter
    • 2 years ago
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    im not sure about the -1

  8. starrhunter
    • 2 years ago
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    there isnt an answer for that... right?

  9. hashsam1
    • 2 years ago
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    |dw:1337100894030:dw|

  10. m_charron2
    • 2 years ago
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    ok, I'll give you that one, because it's a bit tricky, it's actually i. i * i = -1

  11. starrhunter
    • 2 years ago
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    i times i. got it.

  12. m_charron2
    • 2 years ago
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    ok, perfect, so sqrt of -16 = sqrt 16 * sqrt -1 = 4 * i

  13. starrhunter
    • 2 years ago
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    but its negative 16 under the square root....

  14. starrhunter
    • 2 years ago
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    and none of that is one of my choices

  15. starrhunter
    • 2 years ago
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    all of my choices look like fractions

  16. m_charron2
    • 2 years ago
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    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
    • 2 years ago
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    |dw:1337101077852:dw|

  18. starrhunter
    • 2 years ago
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    so it would be

  19. hashsam1
    • 2 years ago
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    |dw:1337101138650:dw|

  20. starrhunter
    • 2 years ago
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    thank you so much for all of your help!

  21. hashsam1
    • 2 years ago
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    is this the answer?

  22. hashsam1
    • 2 years ago
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    in your choices?

  23. starrhunter
    • 2 years ago
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    its 16 + 28i over 65

  24. m_charron2
    • 2 years ago
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    perfect

  25. starrhunter
    • 2 years ago
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    |dw:1337101312782:dw|

  26. starrhunter
    • 2 years ago
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    yay!

  27. hashsam1
    • 2 years ago
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    |dw:1337101388901:dw|

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