If a complex number having absolute value of √2 is making 45° angle with x-axis in third quadrant, then it can be written as –

Question

Question

Answer 1

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 the given complex number.

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

Let z = r (cos θ + i sin θ) is a 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 that and angle with x-axis is 45°.

Since its in the third quadrant -

∴

⇒ [r, θ] =