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CBSE NOTES ⇒ Class 11th ⇒ Mathematics ⇒ 5. Complex Number and Quadratic Equations

5. Complex Number and Quadratic Equations

Polar representation of a complex number


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 (rθ). 

This coordinate (rθ) 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. 

 

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Mathematics Class - 11th

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Study Materials List:

CBSE NOTES ⇒ Class 11th ⇒ Mathematics
1. Sets
2. Relations and Functions
3. Trigonometric Functions
4. Principle of Mathematical Induction
5. Complex Number and Quadratic Equations
6. Linear Inequalities
7. Permutations and Combinations
8. Binomial Theorem
9. Sequences and Series
10. Straight Lines
11. Conic Sections
12. Introduction to Three Dimensional Geometry
13. Limits and Derivatives
14. Mathematical Reasoning
15. Statistics
16. Probability

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