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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.

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  1. Barrelracing
    • one year ago
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    |dw:1437857496870:dw|

  2. carolinar7
    • one year ago
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    |dw:1437846970791:dw|

  3. carolinar7
    • one year ago
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    |dw:1437847013934:dw|

  4. anonymous
    • one year ago
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    |dw:1437846985513:dw|

  5. carolinar7
    • one year ago
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    No you need to multiply it by conjugate

  6. carolinar7
    • one year ago
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    Oh you did, my bad

  7. anonymous
    • one year ago
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    the first thing you have to do is combine the denominator into one complex number. |dw:1437847204733:dw|

  8. anonymous
    • one year ago
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    |dw:1437847105860:dw|

  9. Barrelracing
    • one year ago
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    5 - 2i

  10. anonymous
    • one year ago
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    that's (7 + 2) + (-3i + 5i)

  11. Barrelracing
    • one year ago
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    9 +2

  12. anonymous
    • one year ago
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    9 + 2i, so now you have \[\frac{ \sqrt{-4} }{ 9+2i }\]

  13. anonymous
    • one year ago
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    can you write √-4 in terms of i?

  14. Barrelracing
    • one year ago
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    no

  15. anonymous
    • one year ago
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    \[\sqrt{-4}=\sqrt{4} \times \sqrt{-1}=2i\]

  16. anonymous
    • one year ago
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    ^do you understand that?

  17. anonymous
    • one year ago
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    so now we have \[\frac{ 2i }{ 9+2i }\]

  18. anonymous
    • one year ago
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    and now you can multiply by the conjugate like @carolinar7 said above

  19. Barrelracing
    • one year ago
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    ok I don't know how to do that

  20. anonymous
    • one year ago
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    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
    • one year ago
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    18i - 4/77

  22. Barrelracing
    • one year ago
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    -4+18i/77

  23. anonymous
    • one year ago
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    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
    • one year ago
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    thank you

  25. anonymous
    • one year ago
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    you're welcome

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