Question

The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.

Options

• 1 + 2i

• –1 – 2i

• 2 + i

• –1 + 2i

Answer 1

The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is –1 – 2i.

Explanation:

Given that: z = 2 – i

If z rotated through an angle of `pi/2` about the origin in clockwise direction.

Then the new position = `z.e^(-(pi/2))`

= `(2 - i) e^(-(pi/2))`

= `(2 - i)[cos((-pi)/2) + i sin ((-pi)/2)]`

= (2 – i)(0 – i)

= –1 – 2i