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Math Help - Complex numbers

  1. #1
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    Complex numbers

    Please help me answer both of these questions. Thank you
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by norivea
    Please help me answer both of these questions. Thank you
    1a) Find the real and complex roots of:

    <br />
(z-3)(z^2-5z+8)=0<br />

    This has three roots, one real corresponding to the first factor; so x=3 is a root.

    The other two roots are the roots of the second factor z^2-5z+8=0, these may
    be found using the quadratic formula, which gives in this case:

    <br />
z=\frac{5}{2}\pm \frac{\sqrt{7}}{2}i<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by norivea
    Please help me answer both of these questions. Thank you
    1b) Find the real and complex roots of:

    <br />
z^3-10z^2+34z-40<br />

    given that 3-i is a root.

    A cubic with real coefficients always has at least one real root, and
    complex roots occur in conjugate pairs. So both 3-i and
    3+i are roots. Also:

    <br />
z^3-10z^2+34z-40=(z-(3-i))(z-(3+i))(z-a)<br />

    where a is real, and so easily found to be 4,
    so the remaining root is z=4.

    RonL
    Last edited by CaptainBlack; June 16th 2006 at 04:10 AM.
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