### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Polar representation of Complex Numbers

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: –(i)

Clearly, —(ii)

Now, —(iii)

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: where Example:

Find Solution:  Some Properties in Polar Form: (i) (ii) If and are the two complex numbers expressed by: and then and If , we get:

(i) (ii) (iii) (iv) NOTE:

If , where is an integer or zero.

If , then graphical representation of Example 1:

Express in the form of .

Solution: Example 2:

If and   Scroll to Top