The polar form of complex number  can be written as –

CONCEPT:

Point P is uniquely determined by the ordered pair of real numbers (r, θ), called the polar coordinates of the point P.

P represent the nonzero complex number z = x + iy.

Here  is called the modulus of the given complex number.

The argument of Z is measured from positive x-axis only.

Let z = r (cosθ + i sinθ) is polar form of any complex number then following ways are used while writing θ for different quadrants –

For the first quadrant, 

For the second quadrant 

For the third quadrant 

For the fourth quadrant 

CALCULATION:

Given complex number 

On rationalization we get –

rcosθ = -1, rsinθ = √3 

By squaring and adding, we get –

∴ r = 2

 and 

Since it is in the second quadrant, 

So, on comparing with z = r (cosθ + i sinθ), we can write as