complex numbers

The equation x^2+1=0 has two solutions: x=i ; x=-i. Every equation

P(x)=0 (2)

has at least one solution. The solutions are complex numbers. They are written as an ordered pair a+ib. Another possibilty is to call some solutions "imaginary". I dont see why we should do that. We have other complex enteties like triangulae and points, that we don't call "imaginary". Anyhow, the roots of (2) that can be written "a+i*0" are called "real". These have the characteristic that they can be ordered. Two numbers have the relation 'a is less than b', if they are not identical. Other complex numbers do not have this characteristics. They can be treated in calculus anyhow. Here are some rules:

(a+ib)+(c+id)=((a+c)+i(b+d)

(a+ib)*(c+id)=((ac-bd)+i(ac+bd))