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Factorzing polynomials with complex coefficients

  1. May 18, 2013 #1
    Not sure if this is the right place to post (but its related to a complex analysis questions)

    I'm doing a past paper for my revision and am stuck at the first hurdle. I simply cannot factor this polynomial in z for the life of me. I've tried completing the square and the usual quadratic formula but do not get the answer as given.

    I know what the answers are supposed to be so if anyone could help walk me through how you get there and if there is a technique of generally doing so I'd be most grateful.

    [tex] z^2-(2i+4)z + 8i = (z-4)(z+2i) [/tex]
     
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  3. May 18, 2013 #2

    Office_Shredder

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    Why don't you show us how you tried doing the quadratic formula? Because it should work
     
  4. May 18, 2013 #3
    I can:

    [tex] z1,z2= \frac{(2i+4) \pm \sqrt{(2i+4)^2-(4)(1)(8i)}}{(2)(1)}[/tex]
    this simplifies to:
    [tex]z1,z2 = (i+2) \pm \sqrt{3-4i}[/tex]

    Which isn't what I need...

    Do you get the solutions z = 4 and z = 2i?
     
    Last edited: May 18, 2013
  5. May 18, 2013 #4

    Office_Shredder

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    You did get those numbers. Do you know what the square root of 3-4i is?
     
  6. May 18, 2013 #5
    Hi Shredder - No I didn't know how to take the sqrt of a complex number... but I do now. Thanks for pointing this out - I looked it up and am happy with dealing with these now. Your help is much appreciated!

    Felix
     
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