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Polar representation of a complex number class 11 Mathematics Chapter 5. Complex Number and Quadratic Equations

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5. Complex Number and Quadratic Equations

| Polar representation of a complex number |

Polar representation of a complex number Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study

Polar representation of a complex number:

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

Polar form: Polar form of a complex number is another way to represent a complex number on argand plane.

if z = x + iy is any complex number then

In polar representation a complex number z is represented by two parameters r and θ. Where parameter r is the modulus of a complex number and θ is the angle with the positive direction of x - axis.

using pythagoros theorem

Here Z of modulus = r and θ is called the argument (or amplitude) of z which is denoted by arg z.

Principle arguments of z : The value of θ such that – π < θ ≤ π, called principal argument of z and is denoted by arg z.

The point (x,y) represent a normal cartesian coordinate. But in polar form this point is reoresented by a special coordinate system which is called polar coordinate having (r, θ).

This coordinate (r, θ) represents the each location of a point of a complex number.

So, We have there is a relation between polar cordinates and cartesian coordinates.

We know;

z = Re(z) + Img(z)

Then x-axis represent Re(z) and y-axis represent Img(z).

We consider Origin (0, 0) as pole.

For any complex number z = x + iy is represented as r (cosθ + i sinθ) as any point on complex plane. This is called polar representation of a complex number. Where θ is angle between r and x-axis.

Other Pages of this Chapter: 5. Complex Number and Quadratic Equations

1. Chapter 5. Complex Number and Quadratic Equations | Introduction

2. Chapter 5. Complex Number and Quadratic Equations | Complex Number

3. Chapter 5. Complex Number and Quadratic Equations | Algebra of Complex Numbers

4. Chapter 5. Complex Number and Quadratic Equations | The Modulus and Congugate of a Complex Number

5. Chapter 5. Complex Number and Quadratic Equations | Polar representation of a complex number

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