The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by :

Step-by-step solution

Let P 2 + i       &    S(z) By Rotation theorem, rotating about 3 + 3 i , we get z - 3 + 3 i 3 + i - 3 + 3 i = 2 2 2 e - i π 4 ⇒  z - 3 - 3 i - 2 i = 1 - i ⇒  z - 3 - 3 i = - 2 i - 2 ⇒  z = 1 + i