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anonymous

  • one year ago

Simplify: 3+2i over 4-i

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  1. Nnesha
    • one year ago
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    multiply top and bottom of the fraction by conjugate of the denominator

  2. Nnesha
    • one year ago
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    what is the `conjugate` of 4-i ? do you know ?

  3. anonymous
    • one year ago
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    Welcome to openstudy!

  4. Nnesha
    • one year ago
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    thanks :=)

  5. anonymous
    • one year ago
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    lol

  6. anonymous
    • one year ago
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    I don't know the conjugate ;~;

  7. Nnesha
    • one year ago
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    here is an example the conjugate of a+bi is `a-bi` so change the sign of the imaginary term

  8. anonymous
    • one year ago
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    I don't get how to do that either...

  9. Nnesha
    • one year ago
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    conjugate of a+bi is `a-bi` right so what's the difference btw `a+bi` and `a-bi` ?

  10. anonymous
    • one year ago
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    The + and -

  11. Nnesha
    • one year ago
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    yes right so you should change the sign of imaginary number `i` = imaginary

  12. Nnesha
    • one year ago
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    so what's the conjugate of 4-i ?

  13. anonymous
    • one year ago
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    4+i?

  14. Nnesha
    • one year ago
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    yes right! now multiply \[\huge\rm \frac{ 3+2i }{ 4-i} \times \frac{ 4+i }{ 4+i }\]

  15. anonymous
    • one year ago
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    12+3i over 16?

  16. Nnesha
    • one year ago
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    show ur steps please how did you get that ?

  17. anonymous
    • one year ago
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    I don't know how I did that. I have no idea how i did that.

  18. Nnesha
    • one year ago
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    then why did you post that ?

  19. anonymous
    • one year ago
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    I was hoping it was right..

  20. Nnesha
    • one year ago
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    familiar with the foil method ?

  21. anonymous
    • one year ago
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    Yeah.

  22. Nnesha
    • one year ago
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    i know that's one of ur option.

  23. Nnesha
    • one year ago
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    alright good apply foil method \[\huge\rm \frac{ (3+2i)(4+i) }{ (4-i)(4+i) }\] (3+2i)(4+i) = ??

  24. anonymous
    • one year ago
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    I think it's 12+14i? That's what I got..

  25. Nnesha
    • one year ago
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    okay plz show ur work so i can look over to find out mistakes :=)

  26. Nnesha
    • one year ago
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    that would be great!

  27. anonymous
    • one year ago
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    (3+2i)(4+i) 12+3i+8i+3i 12+6i+8i 12+14i

  28. Nnesha
    • one year ago
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    nice thanks so 2i times i = ??

  29. anonymous
    • one year ago
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    Not 3i?

  30. anonymous
    • one year ago
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    OH OH -2

  31. Nnesha
    • one year ago
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    yes right i times i= i^2 and i^2 =-1 so 2(-1) = -1 now fix it

  32. Nnesha
    • one year ago
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    so it's \[12+3i+8i-2\]

  33. anonymous
    • one year ago
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    So I was mostly right. Now what.

  34. Nnesha
    • one year ago
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    now combine like terms 12+3i+8i-2 = ?

  35. anonymous
    • one year ago
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    10+11i

  36. Nnesha
    • one year ago
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    looks right! now simplify the denominator (4-i)(4+i)= ?

  37. anonymous
    • one year ago
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    17!

  38. Nnesha
    • one year ago
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    right that's denominator so what would be the final answer ?

  39. anonymous
    • one year ago
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    \[\frac{ 10+11i}{ 17}\]

  40. Nnesha
    • one year ago
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    looks good ! great job !

  41. anonymous
    • one year ago
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    Thank you~

  42. Nnesha
    • one year ago
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    np :=)

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