Geometrical Representation of Complex Number

If real scales are chosen on two mutually perpendicular axes X′OX and Y′OY (called the x axis and y axis respectively), you can locate any point in the plane determined by these lines, by the ordered pair of real numbers (a, b) called rectangular co-ordinates of the point.

Since every complex number a + ib can be considered as an ordered pair (a, b) of real numbers, you can represent such number by a point P in the xy plane, called the complex plane. Such a representation is also known as the Argand diagram.

The modulus of the complex number z = a + ib represents the distance between z and the origin.

|z| = √(a² + b²)

To each complex number there corresponds one and only one point in the plane, and conversely to each point in the plane there corresponds one and only one complex number.

The set of real numbers (x, 0) corresponds to the x-axis called real axis. The set of all purely imaginary number (0, y) corresponds to the y-axis called the imaginary number axis. The origin identifies the complex number 0 = 0 + i0.