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marigirl

  • one year ago

question about finding roots of a complex number If we have: find the cube roots of 1 then we can write z= 1(cos 0 + i sin 0) and our values of k can range from 0, 1, 2 But our k values could also be -1, 0 and 1 yes?

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  1. anonymous
    • one year ago
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    its been a while since ive done this but lets have a go

  2. anonymous
    • one year ago
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    cube roots of 1 means this right: \[z ^{3}=1\] right?

  3. marigirl
    • one year ago
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    yes and i did all the values and it looks like this

  4. marigirl
    • one year ago
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    -240 deg (-0.5 + 0.866i) -120 deg (-0.5-0.866i) 0 is 1 120 deg (-0.5 + 0.866i) 240 deg (-0.5 -0.866i)

  5. marigirl
    • one year ago
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    when i did it on the graphics calculator the values i got are: 1 -0.5 + 0.866i -0.5 - 0.866i

  6. anonymous
    • one year ago
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    yep, for a cubic polynomial we should always expect one positive real root and a pair of complex conjugates

  7. anonymous
    • one year ago
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    have you learnt demoviers theorem or what ever?

  8. marigirl
    • one year ago
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    oh yea i used his formula

  9. anonymous
    • one year ago
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    simply apply it for k=0,1,2 and you should find those answers that your calc gave you

  10. marigirl
    • one year ago
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    looking at k values- some youtube clips focus on all positive k values such as 0, 1, 2, some other youtube videos tend to go to negative k values because the angle exceeds 18- deg because arg z has to lie between -pi and +pi for it to be positive. but it doesnt really matter ay because of the cyclic nature of this question

  11. anonymous
    • one year ago
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    correct

  12. marigirl
    • one year ago
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    besides the calculator gives you the correct answer

  13. anonymous
    • one year ago
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    well it depends whether or not the question states you have to use a particular method. If it doesn't, simply use your calcualtor

  14. anonymous
    • one year ago
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    but i would get familiar with the theorems out there so you can grasp the concepts

  15. anonymous
    • one year ago
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    i have to leave now, but focus on this youtube video, id like to explain it myself but unfortunately i have to run a few errands. https://www.youtube.com/watch?v=p39QRoe9QwA

  16. anonymous
    • one year ago
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    good luck

  17. anonymous
    • one year ago
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    my tip is to use the UNIT CIRCLE all the time. it is your friend! Very very very important in this field of math

  18. marigirl
    • one year ago
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    thanks heaps!

  19. anonymous
    • one year ago
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    : )

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