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dumbsearch2

  • one year ago

TRIGONOMETRY: Write z = the square root of 3 minus i. in abbreviated trigonometric form.

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  1. dumbsearch2
    • one year ago
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  2. anonymous
    • one year ago
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    fist find the magnitude?

  3. anonymous
    • one year ago
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    \[Z=x+i y\] \[|Z|=\sqrt{x^2+y^2}\]

  4. dumbsearch2
    • one year ago
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    So I just plug in y as -1 and x as root(3)? That's all there is to it?

  5. anonymous
    • one year ago
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    yes @dumbsearch2

  6. dumbsearch2
    • one year ago
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    Then what?

  7. anonymous
    • one year ago
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    \[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\Theta=\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\] in fourth quarter

  8. dumbsearch2
    • one year ago
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    What is that?

  9. anonymous
    • one year ago
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    |dw:1441111202672:dw|

  10. dumbsearch2
    • one year ago
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    I did: |Z| = root((root(3))^2+(-1)^2) and I found: |Z| = 2. What now?

  11. anonymous
    • one year ago
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    complex number: magnitude + angle

  12. dumbsearch2
    • one year ago
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    How should I proceed? I found that |Z| = 2.

  13. anonymous
    • one year ago
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    this the magnitude, and now we should find the angle

  14. anonymous
    • one year ago
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    \[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\]

  15. anonymous
    • one year ago
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    \[Z=x+iy=re^{i \theta}=r(\cos \theta+isin \theta)\]=\[rCis\] and\[r=|Z|\]

  16. anonymous
    • one year ago
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    r=|Z|=2

  17. anonymous
    • one year ago
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    \[\theta=-30^0=330^0\]

  18. anonymous
    • one year ago
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    Plug values of r & θ in: (rCis θ)

  19. dumbsearch2
    • one year ago
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    Thank you so much! Most importantly, I know how to do the problem by myself now, in the clear manner in which you explained it... thanks a million!

  20. anonymous
    • one year ago
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    @dumbsearch2 no problem, you are welcome in any time.

  21. dumbsearch2
    • one year ago
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    I want to do the same thing for the next problem: "Write z = -5 in abbreviated trigonometric form." However, why isn't there an i? Also how can I find the x and the y for the magnitude if there is only one variable (-5)?

  22. anonymous
    • one year ago
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    I finished complex course since 1 year only. it is interesting.

  23. anonymous
    • one year ago
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    Z=-5+i0

  24. anonymous
    • one year ago
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    x=-5, y=0

  25. dumbsearch2
    • one year ago
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    Thank you!

  26. dumbsearch2
    • one year ago
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    |Z| = 5, right?

  27. anonymous
    • one year ago
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    |dw:1441112765839:dw| not 0

  28. dumbsearch2
    • one year ago
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    5 cis 180 degrees is the solution

  29. dumbsearch2
    • one year ago
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    because a straight line is 180 degrees

  30. dumbsearch2
    • one year ago
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    right?

  31. anonymous
    • one year ago
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    not, the angle is counted from positive x-axis

  32. dumbsearch2
    • one year ago
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    A. 5 cis 180 degrees B. -5 cis 0 degrees C. root(5) cis 180 degrees D. 25 cis 0 degrees

  33. dumbsearch2
    • one year ago
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    Which one?

  34. anonymous
    • one year ago
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    A

  35. dumbsearch2
    • one year ago
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    thank you, I understand now.

  36. anonymous
    • one year ago
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    Good luck

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