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anonymous

  • one year ago

PLEEEEEEEEEEEEEEEEEEEEEEEEEEEASE Check my answer for a medal? Express the complex number in trigonometric form. -2 + 2(square root of three)i I got 4(cos(5pi/6) + i sin(5pi/6))

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  1. anonymous
    • one year ago
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    pls :((((

  2. anonymous
    • one year ago
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    The modulo of the complex number is correct

  3. anonymous
    • one year ago
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    okay so instead of 5pi/6 it should be 2pi/3? I'm not sure why though

  4. anonymous
    • one year ago
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    Correct, its 2pi/3

  5. anonymous
    • one year ago
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    I did arctan (2*sqrt(3) /2)

  6. anonymous
    • one year ago
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    To find the angle of a complex number, you apply the following formula: \[\arg(z) = \frac{ \Im(z) }{ \Re(z) }\]

  7. anonymous
    • one year ago
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    \[\arg(z) = \tan^{-1} \frac{ \Im(z) }{ \Re(z) }\]

  8. anonymous
    • one year ago
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    I missed the arctan in the previous formula.

  9. anonymous
    • one year ago
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    You missed the negative sign in your arctan.

  10. anonymous
    • one year ago
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    arctan (2sqrt(3) / -2)?

  11. anonymous
    • one year ago
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    Correct.

  12. anonymous
    • one year ago
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    converted to radians it's (-pi/3) right? so where does the 2 come from?

  13. anonymous
    • one year ago
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    You will get \[-\frac{ \pi }{ 3 }\]

  14. anonymous
    • one year ago
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    Recall that you can add an angle by 2pi at any time, especially to make it positive.

  15. anonymous
    • one year ago
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    -pi/3 + 2pi = 5pi/3 -pi/3 - 2pi = -7pi/3??? I feel like I'm missing something obvious..:/

  16. anonymous
    • one year ago
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    Well, do recall that arctan, along with other inverse trig functions, is a multi-valued function.

  17. anonymous
    • one year ago
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    -pi/3 is only one of the possible solutions.

  18. anonymous
    • one year ago
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    Remember tangent is negative in both the second and fourth quadrants.

  19. anonymous
    • one year ago
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    I don't know how to find a value in another quadrant if it's not on the unit circle

  20. anonymous
    • one year ago
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    It's on the unit circle. You know that your first solution is -pi/3, which is 5pi/3 in the fourth quadrant.

  21. anonymous
    • one year ago
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    Your second solution must be \[\pi - \frac{ \pi }{ 3 } = \frac{ 2 \pi }{ 3 }\]

  22. anonymous
    • one year ago
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    why do you subtract it from pi?

  23. anonymous
    • one year ago
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    It's the unit circle. You subtract from the quadrant. You subtract from pi for the second quadrant.

  24. anonymous
    • one year ago
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    Oh wow. I never learned that... Thank you so much for your help!

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