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Math Help - Determinants and complex numbers

  1. #1
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    Determinants and complex numbers

    Hey everyone,
    Do you know if there are any links between the property of matrix determinants and Complex numbers.
    - a complex number being z=x+yi, where x and y are real numbers and i is the imaginary number which represents sqrt(-1)
    - a matrix being a 2x2 representation of a Complex number, written as:
    x -y
    y x

    I know how to find the determinant of a matrix, but I don't know if there is a property in Complex number operations etc that corresponds to this determinant property in Matrices.
    ie. if you perform both operations in their different forms with the same complex number/matrix, you should end up with the same result. I've tried and tried different things, but I can't think of anything that is similar.
    I need help! Please and thankyou
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  2. #2
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    Re: Determinants and complex numbers

    Quote Originally Posted by NJoyce View Post
    Hey everyone,
    Do you know if there are any links between the property of matrix determinants and Complex numbers.
    - a complex number being z=x+yi, where x and y are real numbers and i is the imaginary number which represents sqrt(-1)
    - a matrix being a 2x2 representation of a Complex number, written as:
    $M = \left[ {\begin{array}{*{20}{c}}x&{ - y}\\y&x\end{array}} \right]$

    I know how to find the determinant of a matrix, but I don't know if there is a property in Complex number operations etc that corresponds to this determinant property in Matrices.
    The determinate of that matrix is the square of the absolute value of $x+iy$: $|M|=x^2+y^2=|x+iy|^2$.

    I don't know what exactly you are driving for.
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