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Thread: Complex Numbers Question HELPPPP !!!

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    Question Complex Numbers Question HELPPPP !!!

    a) Determine the roots of z^4 + 1 = 0 in cartesian form. Plot them on an Argand diagram.
    b) Write z^4 + 1 in terms of real quadratic factors/
    c) Divide by z^2 to show that cos(2x) = (cos(x) - cos(45)(cos(x) - cos(135))

    Need help with part (c) thanks

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    Re: Complex Numbers Question HELPPPP !!!

    Quote Originally Posted by _mysteryatar_ View Post
    a) Determine the roots of z^4 + 1 = 0 in cartesian form. Plot them on an Argand diagram.
    b) Write z^4 + 1 in terms of real quadratic factors/
    c) Divide by z^2 to show that cos(2x) = (cos(x) - cos(45)(cos(x) - cos(135))

    Need help with part (c) thanks
    pretty sure it should be 1/2 cos(2x) for (c)



    meant to write x instead of theta rip

    Incase you get confused in the 3rd line, I divided the terms of each factor on the RHS by z (which accounts to dividing the whole side by z^2)
    Last edited by jathu123; 22 Oct 2018 at 6:13 PM.
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    Re: Complex Numbers Question HELPPPP !!!

    thank you, i didnt write part (c) wrong by the way i think you read it wrong because it says: [2](cos(x) + cos(45))(cos(x) + cos(135))

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    Re: Complex Numbers Question HELPPPP !!!

    Quote Originally Posted by _mysteryatar_ View Post
    thank you, i didnt write part (c) wrong by the way i think you read it wrong because it says: [2](cos(x) + cos(45))(cos(x) + cos(135))
    Quote Originally Posted by _mysteryatar_ View Post
    a) Determine the roots of z^4 + 1 = 0 in cartesian form. Plot them on an Argand diagram.
    b) Write z^4 + 1 in terms of real quadratic factors/
    c) Divide by z^2 to show that cos(2x) = (cos(x) - cos(45)(cos(x) - cos(135))

    Need help with part (c) thanks
    no worries!
    lol idk if im blind or my laptop display is being dodgy
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    Re: Complex Numbers Question HELPPPP !!!

    Not sure this hangs together properly?
    When you say z^4+1=(z^2-root2z+1)(z^2+root2z+1) this is a factorization of a polynomial. It is an identity true for every complex z.

    Suddenly in the next line you are assuming that |z|=1?

    For example if z=7 then most certainly 49+1/49 is not 2cos(anything)?

    Proof as it stands is quite muddy and misleading.

    Best to at least state somewhere that you are restricting the identity to the unit circle.
    Last edited by peter ringout; 20 Nov 2018 at 11:39 PM.

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