introduction on complex numbers

Complex numbers:
In this chapter,we survey the algebraic and geometric structure of the complex numbers system,we assume various
numbers system,we assume various corresponding properties of real numbers to be known.
Complex numbers can be defined as order pairs (x,y) of real numbers coordinates x and y ,when real numbers x are displayed as points(x,0) on the real axis,it is clear that the set of complex numbers includes the real numbers as a subset,
Complex numbers of the form(0,y) correspond to points on the y axis are called pure imaginary numbers the y axis is then referred as the imaginary axis ,so that z=(x,y),the real numbers x and y ,moreover known as the real and imaginary parts of z,so that
Rez=x & Imz=y
It is natural to associate any non zero complex number z=x+iy with the direction line segment ,or vector from the origin to the point (x,y) that represent z ,in the complex plane ,in fact we often refer to z as the point z or the vector z in the number z=x+iy and z=-x+iy are displayed graphically as both points and radius vector