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Math Help - Complex Numbers help

  1. #16
    Super Member ILikeSerena's Avatar
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    Re: Complex Numbers help

    Quote Originally Posted by kmalik001 View Post
    Thank you so much!
    I understand it.

    I am also kind of stumped on this question.

    Determine the only real values a, b, c and d such that the equation:
    z^4 + az^3 + bz^2 + cz + d = 0
    has both z1 and z2 as roots.

    I don't really get what this is asking.
    Good!

    I guess this requires a bit of additional knowledge about polynomial equations with real coefficients and complex roots.

    A polynomial that has both z1 and z2 as its roots, must be of the form:

    (z-z1)(z-z2)(...) = 0

    If such an equation has only real coefficients, that implies that not only z1 must be a root, but also its conjugate z1*.
    (I suspect that is somewhere in your notes.)

    In other words, your equation must be of the form:

    (z-z_1)(z-z_1^*)(z-z_2)(z-z_2^*) = 0

    If you expand this, which coefficients do you get?
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  2. #17
    Super Member ILikeSerena's Avatar
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    Re: Complex Numbers help

    Quote Originally Posted by Plato View Post
    @ ILikeSerena
    I don't care that you responded to this thread.
    Ah well, that's okay, as long as you don't mind if I slice your comments to pieces (assuming you give me the opportunity as you did this time round).
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  3. #18
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    Re: Complex Numbers help

    Ah yes I see what you are doing. So when I expanded it I get z^4 + 4z^3 + 0z^2 -200z + 500. Which I hope is right.
    I expanded (z^2 -6z + 10)(z^2 +10 z +50), which I know are right since their solutions are the z1, z2 and their conjugates.

    Thanks to both of you once again
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  4. #19
    Super Member ILikeSerena's Avatar
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    Re: Complex Numbers help

    Quote Originally Posted by kmalik001 View Post
    Ah yes I see what you are doing. So when I expanded it I get z^4 + 4z^3 + 0z^2 -200z + 500. Which I hope is right.
    I expanded (z^2 -6z + 10)(z^2 +10 z +50), which I know are right since their solutions are the z1, z2 and their conjugates.

    Thanks to both of you once again
    Yep. That is right!
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  5. #20
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    Re: Complex Numbers help

    So there is another complex number question.

    u = −1 + j√3 and v = √3 − j

    Let a be a real scaling factor. Determine the value(s) of a such that
    |u −a/v | = 2√2

    So this is what I am doing I am kind of stuck and wondering if I am on the right track.
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  6. #21
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    Re: Complex Numbers help

    Complex Numbers help-image.jpg
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