2x2 complex matrices
|* we take a complex 2x2 matrix, [a1+ia2
c1+ic2 d1+id2 ] The determinant is | a1 b1| - |a2 b2| + i |a1 b1| +i |a2 b2|
| c1 d1| |c2 d2| |c2 d2| |c1 d1| . In the real part, there are 2 sub parts which are subtracted from each other and in the imaginary parts, there are 2 sub parts which are added. In the real sub-part, the matrices are pure i.e. either they are from real (a1,b1,c1,d1) or from imaginary component (a2,b2,c2,d2). In the imaginary sub-part, the matrices are mixed i.e 2 from real (a1,b1; or c1,d1) + 2 from imaginary (a2,b2; or c2,d2) components.
|*if x+iy is a complex number, then √( x+iy) = ( x2+y2)1/4 * [cos [(atan(x/y))/2] +i [sin [(atan(x/y))/2] as per De Moivre Theorem.|