complex z plane


We have seen that there is a (1,-1) correspondence between the element (ordered pair) of the complex z plane RXR and the complex numbers. Therefore, there is a (1,-1) correspondence between the points of the complex z plane and the complex numbers. We can, therefore, represent complex number by the point of the coordinate plane. In this representation, every complex number will be represented by one and only one point of the complex z plane, and every point of the plane will represent one and only one complex number. The component of the complex number will be the coordinate of the point represent of the point representing it.

Complex Z plane



coordinate plane is called the COMPLEX  Z- PLANE or Argand PLANE

(i) Real  x-axis

In representation of coordinate plane, X- AXIS  is called real axis.

A point on the x-axis is called the real number

(ii) Imaginary, y-axis

In representation of coordinate plan plane, y- AXIS  is called imaginary axis.

A point on the y-axis is called the imaginary number

(iii) x, y coordinate point

x, y are the coordinate  of the point. It represents the complex number.

Modulus of complex number (a+ι b)

The real number \sqrt{x^{2{}}+y^{2}}  is called the modulus of complex number a+ι b

modulus formula proof:



modulus of complex number a+Ι b

in the figure line MA is perpendicular to o x line

(iv) Modulus of complex number sign    |z|

modulus of complex number, generally denoted by

modulus complex number sign

The modulus of the complex number is the distance from the origin of the point

representing the number.

\large z=x+\iota y=(x,y)\, \, then

modulus of z equal to

modulus of complex number


fined the modulus of the following complex number

(i)  1-  ι√3


z=  1-  ι√3

or z= 1-  ι (√3)

 complex z plane modulus of complex number

this is equal to = \large \sqrt{1+3}=2