Question

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

A. 1 + 2i
B. –1 – 2i
C. 2 + i
D. –1 + 2i

Answer 1

B. -1 – 2i

Given z = 2 – i

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

Then the new position = z. e^-(π/2)

= (2 – i) e^-(π/2)

= (2 – i) [cos (-π/2) + i sin (-π/2)]

= (2 – i) (0 – i)

= -1 – 2i