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anonymous

  • one year ago

True or False: When its argument is restricted to [0, 2pi), the polar form of a complex number is not unique.

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  1. anonymous
    • one year ago
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    I think it's false

  2. freckles
    • one year ago
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    |dw:1438653320969:dw| let's think about rewriting this polar coordinate so that theta is between 0 and 360

  3. freckles
    • one year ago
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    |dw:1438653367482:dw|

  4. freckles
    • one year ago
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    but what happens when you change the sign of that other r

  5. freckles
    • one year ago
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    for example where is (-3,225 deg)

  6. anonymous
    • one year ago
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    \[(3\sqrt{2}/2, 3\sqrt{2}/2)\] ?

  7. anonymous
    • one year ago
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    wait it would be -3root2/2, -3root2/2 right?

  8. freckles
    • one year ago
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    |dw:1438653913563:dw| I was going for that if you change the sign of the r it goes in the opposite direction on that same line there

  9. anonymous
    • one year ago
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    Oh okay yes

  10. freckles
    • one year ago
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    if you want to write both and Cartesian coordinates you can... \[(r=3,\theta=45 \deg) \\ x=r cos(\theta)= 3 \cos(45) =3 \frac{\sqrt{2}}{2} =\frac{ 3 \sqrt{2}}{2} \\ y =r \sin(\theta)= 3 \sin(45) =3 \frac{\sqrt{2}}{2}= \frac{3 \sqrt{2}}{2} \\ (r=-3, \theta=225 \deg) \\ x =rcos(\theta)=-3 \cos(225)=-3 \frac{-\sqrt{2}}{2}=\frac{3 \sqrt{2}}{2} \\ y=r \sin(\theta)= -3 \sin(225) -3 \frac{-\sqrt{2}}{2}=\frac{3 \sqrt{2}}{2}\]

  11. freckles
    • one year ago
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    as you they both converted to the same Cartesian coordinate pair

  12. freckles
    • one year ago
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    and both have their theta's between 0 and 360 deg

  13. anonymous
    • one year ago
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    So they are not all unique

  14. freckles
    • one year ago
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    When its argument is restricted to [0,2pi), we can still find 2 polar points one with a negative r and one with a positive r. So not unique. If they had said: When its argument is restricted to [0,2pi) where r>0, then the polar coordinate is unique.

  15. freckles
    • one year ago
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    If they had said: When its argument is restricted to [0,2pi) where r>0, then the polar coordinate is unique. then this would be true <---forgot to add this last line

  16. anonymous
    • one year ago
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    Okay so it would be true

  17. anonymous
    • one year ago
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    Awesome! Thank you so much

  18. freckles
    • one year ago
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    right not unique unique means we can only find one but we found two

  19. anonymous
    • one year ago
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    hmmm @freckles it was false. Should I ask my teacher if the question is wrong?

  20. freckles
    • one year ago
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    it is true since \[(r,\theta)=(-r, \theta+\pi) \text{ if } \theta \in [0,\pi) \\ (r,\theta)=(-r,\theta-\pi) \text{ if } \theta \in [\pi,2\pi]\]

  21. freckles
    • one year ago
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    yep in either case there is no one way to write the complex number with restriction that theta has to be between 0 and 2pi

  22. anonymous
    • one year ago
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    Ya I understand the explanation. Should be right. So I'll just have to ask her next time I see her! Thank you for your help!

  23. freckles
    • one year ago
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    np

  24. freckles
    • one year ago
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    http://openstudy.com/study#/updates/53796108e4b0e5430795a83f this question is almost the same question

  25. freckles
    • one year ago
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    i wonder if maybe they were just changing things on the homework to make it not identical but maybe forgot to change some of the answers

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