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Roots of Complex Polynomials

  1. Jan 24, 2006 #1
    Question that I came across and that has stumped me for about a week hehe.
    Let [tex]p(z)=z^n +i z^{n-1} - 10[/tex]

    if [tex]\omega_j[/tex] are the roots for j=1,2,...,n

    compute: [tex]\sum_{j=1}^n \omega_j}[/tex]


    [tex]\prod_{j=1}^n \omega_j}[/tex]
    Last edited: Jan 24, 2006
  2. jcsd
  3. Jan 24, 2006 #2
    Let's consider an easier example first. Let f(x) = x^2 + 3x + 5. If f has roots a and b, then

    x^2 + 3x + 5 = f(x) = (x - a)(x - b) = x^2 + x(-a - b) + ab.

    Hence a + b and ab equal what? Now generalize.
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