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Math Help - Polynomial Complex Numbers

  1. #1
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    Polynomial Complex Numbers

    Hi! First off, great forum, used it as a guide for quite some time

    So, got a problem, polynomials isnt my strongest suit i guess, so here goes:

    Find all the complex solutions to the equation:
    z^4 − z^2 + 3 = 0

    Then factorize z^4 − z^2 + 3, first in complex first grade polynomials, then in second grade?
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by dnm40 View Post
    Hi! First off, great forum, used it as a guide for quite some time

    So, got a problem, polynomials isnt my strongest suit i guess, so here goes:

    Find all the complex solutions to the equation:
    z^4 − z^2 + 3 = 0

    Then factorize z^4 − z^2 + 3, first in complex first grade polynomials, then in second grade?
    Set z^2 = w, say. Then you have a quadratic in w.

    This will give you an equation where z^2 equals either of two values, as given by the standard way of solving a quadratic. Which gives you 2 values of z for each.
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