# Thread: Determinants and complex numbers

1. ## 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

2. ## Re: Determinants and complex numbers

Originally Posted by NJoyce
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.