A complex number  z = x + i y  is the ordered pair  ( x, y )  of real numbers, which can be considered as the Cartesian coordinates of a point in the  xy-plane.

Therefore, any complex number can be graphically represented by a unique point on the coordinate plane of two-dimensional Cartesian coordinate system.

There is one-to-one correspondence between the set of complex numbers and points in the  xy-plane: every point in the complex plane corresponds to a unique complex number, and vice versa.

All real numbers are represented by the points on the x-axis, while all purely imaginary numbers are represented by the points on the y-axis.

These axes are known as the Real and Imaginary Lines, correspondingly.

Complex numbers are added and subtracted in the same way as vectors:

From the geometrical point of view, the absolute value | z | is the distance from the point  z  to zero-point in the complex plane.

The absolute value  | z1 - z2|  is the distance between points  z1  and  z2  in the complex plane.

Index Real Numbers Complex Numbers Exponentiation Algebraic Transformations Algebraic Equations and Ineualities Functions Discrete Algebra Basic Formulas Graphics of Basic Functions