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?
Stacey Warren - Expert brainly.com
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its been a while since ive done this but lets have a go
cube roots of 1 means this right:
yes and i did all the values and it looks like this
when i did it on the graphics calculator the values i got are:
-0.5 + 0.866i
-0.5 - 0.866i
yep, for a cubic polynomial we should always expect one positive real root and a pair of complex conjugates
have you learnt demoviers theorem or what ever?
oh yea i used his formula
simply apply it for k=0,1,2 and you should find those answers that your calc gave you
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
besides the calculator gives you the correct answer
well it depends whether or not the question states you have to use a particular method. If it doesn't, simply use your calcualtor
but i would get familiar with the theorems out there so you can grasp the concepts
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.
my tip is to use the UNIT CIRCLE all the time. it is your friend! Very very very important in this field of math