Argand Plane / Complex Plane:
The plane that has a complex number assigned to each of its points is called the Complex plane or Argand Plane.
The x-axis and the y-axis in the Argand plane are called,respectively the real axis and the imaginary axis.
The identification of a complex number on a plane was proposed by Jean-Robert Argand (1768-1822), hence the complex plane is known as the Argand plane.
Polar Representation of a Complex Number
Let the point have a polar coordinates .
Since has a cartesian we have:
For any value of (i), (ii) and (iii) holds is called an Argument of denoted by , when , is not defined.
A unique value to by restricting to the interval i.e., , then it is called the Principal Argument.
is determined as follows:
Some Properties in Polar Form:
If and are the two complex numbers expressed by:
If , we get:
If , where is an integer or zero.
If , then graphical representation of
Express in the form of .