Mathematics, Engineering, Applied Mathematics.
(a,b), where we define addition of two complex numbers as (a,b)+(c,d)=(a+c,b+d) and multiplication as (a,b) x (c,d)=(ac-bd,ad+bc). Hence, (0,1) is the imaginary unit, i and (1,0) is the usual real number, 1. Writing (a,b) in this fashion is equivalent to writing a+bi, and once we have defined