Definition 1.1.6: Complex Numbers |
The set of complex numbers C is defined as the set of all pairs (x,y) , x, y R, where for z = (x,y) and w = (u, v) we define: |
Note that two complex numbers being equal results in two equations that need to be true simultaneously. You should also observe that we have defined equality of two complex numbers, but not inequality. In other words, we can not decide if one complex number is less or greater than another!