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AHH! complex numbers how to find roots for this equation?

  1. Mar 6, 2006 #1
    find the four roots of the equation
    z^4 + 7 -24i = 0

    completely lost, some help plz...
     
  2. jcsd
  3. Mar 6, 2006 #2
    ohhhh

    z^4 = -7 + 24i....
    = 25cis *** something
     
  4. Mar 6, 2006 #3
    MANY WAYS TO DO THIS.


    you can write it as a exponent.
    z^4 + 7 -24i = 0
    z^4 = - 7 +24i

    Z = Cos(2*n*pi+ theta) + i Sin(2*n*pi + theta) = exponent(i*(theta+2*n*pi))
    n = 0, 1,2,3,
    so
    Z^4 = exponent(i*(theta+2*n*pi)*4)
    = Cos((theta+2*n*pi)*4) + i Sin((theta+2*n*pi)*4) (De Moivre's theorem)


    now you can compare the coefficeints of real /imaginary parts to find theta.
    YOU SHOULD GET A SET OF SOLUTIONS. 4 unique as you substitiute n=0,1,2,3. then they'll repeat for n>3).
     
    Last edited: Mar 6, 2006
  5. Mar 6, 2006 #4

    Hurkyl

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    I bet you know how to solve x^4 - 17 = 0. Why not do the same thing for your problem?
     
  6. Mar 6, 2006 #5
    Ohhh yeah..... thanksss!! i think i mighta got it jolly... not sure coz i used cis not exponent

    hurkyl... reali? because the 'i' made it confusing
     
    Last edited: Mar 6, 2006
  7. Mar 6, 2006 #6

    Hurkyl

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    Yes, really! (7 - 24i) is just a number. Give it a name, like c, if it helps. and z^4 + (7-24i) = 0 (i.e. z^4 + c = 0) is just an ordinary polynomial equation.

    The only difference (at least for this problem) is that it takes more work to simplify an expression involving a root.
     
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