If rectangular form of complex number is shown as  then its polar form is represented as – 

CONCEPT:

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

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

Here  is called modulus of 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 first quadrant,

For second quadrant

For third quadrant

For fourth quadrant

CALCULATION:

Given complex number is

By squaring and adding, we get –

∴ r = 5

 and

Since it is in first quadrant,

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