marigirl
  • marigirl
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
its been a while since ive done this but lets have a go
anonymous
  • anonymous
cube roots of 1 means this right: \[z ^{3}=1\] right?
marigirl
  • marigirl
yes and i did all the values and it looks like this

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marigirl
  • marigirl
-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)
marigirl
  • marigirl
when i did it on the graphics calculator the values i got are: 1 -0.5 + 0.866i -0.5 - 0.866i
anonymous
  • anonymous
yep, for a cubic polynomial we should always expect one positive real root and a pair of complex conjugates
anonymous
  • anonymous
have you learnt demoviers theorem or what ever?
marigirl
  • marigirl
oh yea i used his formula
anonymous
  • anonymous
simply apply it for k=0,1,2 and you should find those answers that your calc gave you
marigirl
  • marigirl
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
anonymous
  • anonymous
correct
marigirl
  • marigirl
besides the calculator gives you the correct answer
anonymous
  • anonymous
well it depends whether or not the question states you have to use a particular method. If it doesn't, simply use your calcualtor
anonymous
  • anonymous
but i would get familiar with the theorems out there so you can grasp the concepts
anonymous
  • anonymous
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
anonymous
  • anonymous
good luck
anonymous
  • anonymous
my tip is to use the UNIT CIRCLE all the time. it is your friend! Very very very important in this field of math
marigirl
  • marigirl
thanks heaps!
anonymous
  • anonymous
: )

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