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gfields444

  • 3 years ago

How would i rationalize 6/ 3+i

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  1. Outkast3r09
    • 3 years ago
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    multiply by the conjugate

  2. Outkast3r09
    • 3 years ago
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    multiply by 1 using the conjugate*

  3. estudier
    • 3 years ago
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    * top n bottom by 3-i

  4. gfields444
    • 3 years ago
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    So 9i?

  5. estudier
    • 3 years ago
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    6(3-i) / (3+i)(3-i)

  6. gfields444
    • 3 years ago
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    Is that all that I have to do? I'm not really sure how to do these sorts of problems

  7. estudier
    • 3 years ago
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    You need to multiply out the brackets and simplify if possible

  8. estudier
    • 3 years ago
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    Just like normal except you have i's to deal with...

  9. gfields444
    • 3 years ago
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    6(3-i)? Wouldn't the bottom cancel itself out?

  10. estudier
    • 3 years ago
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    It is a kind of trick to get rid of the i on the bottom.....

  11. estudier
    • 3 years ago
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    Similar to how you get rid of a rdical, same sort of idea...

  12. gfields444
    • 3 years ago
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    So confused

  13. estudier
    • 3 years ago
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    Multiply it out and you will see...

  14. gfields444
    • 3 years ago
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    9-i/9

  15. gfields444
    • 3 years ago
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    which you could divide 9 by 9 to get one, so -i?

  16. estudier
    • 3 years ago
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    6(3-i) is 18-6i Where do you get 9-i from?

  17. gfields444
    • 3 years ago
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    Oh wow opps. haha I added.

  18. estudier
    • 3 years ago
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    Ok, now what do you get for the bottom?

  19. gfields444
    • 3 years ago
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    9?

  20. estudier
    • 3 years ago
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    You have (3+i)(3-i) Tell me how it comes to 9

  21. gfields444
    • 3 years ago
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    You multiply and the +i and -i cancel out? i'm really sorry, this is new to me haha

  22. estudier
    • 3 years ago
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    (3+i)(3-i) is 3*3 + 3*i -3*i - i^2 (using FOIL?)

  23. estudier
    • 3 years ago
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    So the 3i's cancel out and leave 9-i^2 So what is i^2 ?

  24. gfields444
    • 3 years ago
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    -1

  25. estudier
    • 3 years ago
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    Right, so what is the bottom ( hint-it is not 9)

  26. gfields444
    • 3 years ago
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    8?

  27. estudier
    • 3 years ago
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    9-(-1)

  28. gfields444
    • 3 years ago
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    10

  29. estudier
    • 3 years ago
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    Ok so finally you have 18-6i/10 which you can divide by 2 to get 9-3i/5 as a final answer.

  30. estudier
    • 3 years ago
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    So, procedure for these is *by conjugate top and bottom then simplify

  31. gfields444
    • 3 years ago
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    thank you so much!!!

  32. estudier
    • 3 years ago
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    ur welcome

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