Chapter-5. Complex Number and Quadratic Equations Mathematics class 11 in english Medium CBSE Notes

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. 

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 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.