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    Studying nth roots of unity at the moment, and I'm stuck with finding the complex solutions to the following:

    16z^4 = (z-1)^4

    I get to:

    2z = i(z-1)

    But don't know where to go from there.
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    (Original post by Haza100)
    Studying nth roots of unity at the moment, and I'm stuck with finding the complex solutions to the following:

    16z^4 = (z-1)^4

    I get to:

    2z = i(z-1)

    But don't know where to go from there.
    post your workings are there are more than 1 method for doing this
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    (Original post by TeeEm)
    post your workings are there are more than 1 method for doing this
    16z^4 = (z-1)^4

    2z = \sqrt[4]{1} (z-1)

    \sqrt[4]{1} = 1, -1, i, -i

    Solving for real solutions gives z=1/3 and z=-1

    Can't seem to rearrange for z to get complex solutions, I must be being stupid... all help appreciated.
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    (Original post by Haza100)
    16z^4 = (z-1)^4

    2z = \sqrt[4]{1} (z-1)

    \sqrt[4]{1} = 1, -1, i, -i

    Solving for real solutions gives z=1/3 and z=-1

    Can't seem to rearrange for z to get complex solutions, I must be being stupid... all help appreciated.
    one approach using elementary techniques you can find on page 35 on this link
    http://www.madasmaths.com/archive/ma..._questions.pdf
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    (Original post by TeeEm)
    one approach using elementary techniques you can find on page 35 on this link
    http://www.madasmaths.com/archive/ma..._questions.pdf
    Thanks mate, that helped a lot. Haven't done much math recently so stupidly couldn't see how to rearrange it for z.
 
 
 
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