Difference between revisions of "Argand Plane and Polar Representation"

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The complex number <math>x+iy</math> which corresponds to the ordered pair <math>(x,y)</math>is represented geometrically as the unique point <math>(x,y)</math> in the <math>XY</math>-plane.
The complex number <math>x+iy</math> which corresponds to the ordered pair <math>(x,y)</math>is represented geometrically as the unique point <math>(x,y)</math> in the <math>XY</math>-plane.
In the Fig 4.1.some complex number corresponding to the ordered pairs have been represented geometrically  the points mentioned in the below table.
{| class="wikitable"
|+
!Complex Numbers
!Ordered Pair
!Point
|-
|<math>2+4i</math>
|<math>(2,4)</math>
|<math>A</math>
|-
|<math>-2+3i</math>
|<math>(-2,3)</math>
|<math>B</math>
|-
|<math>0+1i</math>
|<math>(0,1)</math>
|<math>C</math>
|-
|<math>4+0i</math>
|<math>(4,0)</math>
|<math>D</math>
|-
|<math>-4-2i</math>
|<math>(-4,-2)</math>
|<math>E</math>
|-
|<math>1-2i</math>
|<math>(1,-2)</math>
|<math>F</math>
|}

Revision as of 13:32, 9 November 2023

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

Argand Plane
Fig.1 - Argand Plane

We all know that the pair of numbers can be represented on the plane, where is called abscissa and is called the ordinate.

Similar to the -axis and -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

The complex number which corresponds to the ordered pair is represented geometrically as the unique point in the -plane.

In the Fig 4.1.some complex number corresponding to the ordered pairs have been represented geometrically the points mentioned in the below table.

Complex Numbers Ordered Pair Point
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