I know that a complex number of form a+ib can be represented by a 2x2 matrix i.e. [a b;-b a]. They are isomorphic for basic arithmetic operation +,-,x,/.
I wonder how does one perform trigonometric operation using the matrix representation?
Obviously sin(1+2i) is not the same as simply taking sin([1 2;-2 1]).
Can someone familiar in this area enlighten me a bit please?