Argand Plane and Polar Representation

Argand Plane or Complex Plane is the plane formed by the complex numbers.

We all know that the pair of numbers $(x,y)$ can be represented on the $XY$ plane, where $X$ is called abscissa and $Y$ is called the ordinate.

Similar to the $X$-axis and $Y$-axis in two-dimensional geometry, there are two axes in the Argand plane.

• The axis which is horizontal is called the real axis
• The axis which is vertical is called the imaginary axis

Definition

The plane having a complex number assigned to each of its point is called the complex plane or the Argand plane.

Polar Representation

The complex number $x+iy$ which corresponds to the ordered pair $(x,y)$is represented geometrically as the unique point $(x,y)$ in the $XY$-plane.

Fig.1 - Argand Plane

In the Fig 1.some complex number corresponding to the ordered pairs have been represented geometrically by the points mentioned in the below table.

Complex Numbers	Ordered Pairs	Points
$2+4i$	$(2,4)$	$A$
$-2+3i$	$(-2,3)$	$B$
$0+1i$	$(0,1)$	$C$
$4+0i$	$(4,0)$	$D$
$-4-2i$	$(-4,-2)$	$E$
$1-2i$	$(1,-2)$	$F$