Our CBSE Notes for Polar representation of a complex number Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study is the best material for English Medium students cbse board and other state boards students.

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

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

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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

**. Where parameter**

*θ**is the modulus of a complex number and*

**r***is the angle with the positive direction of x - axis.*

**θ**

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).***T****his**** 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

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

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