Complex Numbers |

Basic Definitions Algebraic Operations Complex Conjugation
The Complex Plane Complex Numbers in Polar Coordinate System The Euler Formula Trigonometric Applications Algebraic Applications
Complex Roots |
The Complex Plane
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 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. |