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Math Help - Complex number quadratic equation excercise

  1. #1
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    Greece
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    Complex number quadratic equation excercise

    Given the fact that 1 + i√3 is the root of f(z) = κz + λ where κ,λ belong to R I am asked to find κ and λ. I already know the correct way to solve this but I would like to know why my approach is incorrect.

    Heres what I thought of,

    (
    1 + i√3)κ + λ = 0

    κ + κi
    √3 + λ = 0

    (κ + λ) + (κ
    √3)i = 0

    (κ + λ) = 0 and √3) = 0

    κ = 0 and λ = 0



    PS: Forgive me if I explained and/or presented anything the wrong way, I was taught this in greek and my english math vocabulary is quite poor. Thanks in advance.
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  2. #2
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    Re: Complex number quadratic equation excercise

    The problem stems from the fact that you have a linear polynomial with real coefficients and you want a complex (non-real) solution. If k \neq 0 then \lambda must be a complex number in order for 1+i\sqrt{3} to be a root of kz+\lambda.

    That said, what you've written is good. You've shown that the only way for this complex number to be a root of this real polynomial is for both the coefficients to be 0. Now, I suspect you are actually supposed to have a quadratic polynomial.
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  3. #3
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    Re: Complex number quadratic equation excercise

    Indeed this was the second part of the exercise, in the first part I was given polynomial f(z) = - 2z + 3 where z belongs to C and was asked to solve f(z) = 0. z1 was 1 + i√2 and z2 was 1 - i√2 and since in the second part I was told 1 + i√3 is the root I thought f(z) now was a different polynomial ( κz + λ ).

    Also I noticed you use codecogs equation editor, is it integrated somewhere in this forum or do you use the standalone and then copy the gifs ?
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  4. #4
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    Re: Complex number quadratic equation excercise

    It's integrated. Write TEX /TEX with square brackets "[", "]" around each to make it act like $$ in LaTeX.
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