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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?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its been a while since ive done this but lets have a go

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cube roots of 1 means this right: \[z ^{3}=1\] right?

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1yes and i did all the values and it looks like this

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1240 deg (0.5 + 0.866i) 120 deg (0.50.866i) 0 is 1 120 deg (0.5 + 0.866i) 240 deg (0.5 0.866i)

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1when i did it on the graphics calculator the values i got are: 1 0.5 + 0.866i 0.5  0.866i

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep, for a cubic polynomial we should always expect one positive real root and a pair of complex conjugates

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0have you learnt demoviers theorem or what ever?

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1oh yea i used his formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0simply apply it for k=0,1,2 and you should find those answers that your calc gave you

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1looking 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

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1besides the calculator gives you the correct answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well it depends whether or not the question states you have to use a particular method. If it doesn't, simply use your calcualtor

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i would get familiar with the theorems out there so you can grasp the concepts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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
 one year ago
Best ResponseYou've already chosen the best response.0my tip is to use the UNIT CIRCLE all the time. it is your friend! Very very very important in this field of math
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