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    Hi I have something i may forgetting from Fp1 and now we are at Fp2 complex number. modulus(z+1)^3=-1. When i solve it to get 3 roots, i get -1/2 + (root3)/2, -2, -1/2 - (root3)/2, so i draw them on argand diagram, part c says these three points are on a circle find centre and radius.

    So i look at solution, it says w^3=-1 with centre (0,0) and radius 1...how and where is this from? I thought we can only do this is modulus is with it, then they did w=z+1, as w is translated by (-1 0) solution is centre (-1 0) radius 1.

    I am missing a lot of reasoning behind the steps, don't get the thinking behind w^3=1 being a circle and with radius 1...I understand the translation part.
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    (Original post by Ilovelovelegends)
    Hi I have something i may forgetting from Fp1 and now we are at Fp2 complex number. modulus(z+1)^3=-1. When i solve it to get 3 roots, i get -1/2 + (root3)/2, -2, -1/2 - (root3)/2, so i draw them on argand diagram, part c says these three points are on a circle find centre and radius.

    So i look at solution, it says w^3=-1 with centre (0,0) and radius 1...how and where is this from? I thought we can only do this is modulus is with it, then they did w=z+1, as w is translated by (-1 0) solution is centre (-1 0) radius 1.

    I am missing a lot of reasoning behind the steps, don't get the thinking behind w^3=1 being a circle and with radius 1...I understand the translation part.
    Can you check you posted the question correctly? Something isn't right unless I'm being stupid.
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    that is the question. I did look at solution but i am just confused on why it is a circle without modulus.
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    (Original post by Ilovelovelegends)
    that is the question. I did look at solution but i am just confused on why it is a circle without modulus.
    You would have received a response much faster if you posted the correct question (your post said there was a modulus in the equation).

    I can't help tonight but I'll take a look tomorrow if no one has helped by then. If you want a quicker response then it may be worth starting a new thread (that includes the correct question in the first post) and leaving it unanswered.
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    well i will probably post this again but if u can take a took then pls do...my question was why is w^3=-1 a circle with centre (0,0) radius 1, I mentioned modulus because I was thinking it could also be a a centre if there was a modulus applied to it. Thanks anyways.
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    (Original post by Ilovelovelegends)
    well i will probably post this again but if u can take a took then pls do...my question was why is w^3=-1 a circle with centre (0,0) radius 1, I mentioned modulus because I was thinking it could also be a a centre if there was a modulus applied to it. Thanks anyways.
    w^3=-1 does not describe a circle on the complex plane. You should notice that the sols to this lie on a circle with equation |w|=1, so if w=z+1 we have |z+1|=1 as the circle containing all the solutions to (z+1)^3=-1, and this is a circle of radius 1 and centre (-1,0)

    If they wrote (z+1)^3=-1 for their answer, or whatever, then it's wrong, and I've seen this resource being wrong plenty of times. The correct answer is:

    Centre: (-1,0)
    Radius: 1
    With equation: |z+1|=1
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    Thank you. I just got confused because this question was in the chapter before and thought there was another way to do it expect by use of modulus.
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