The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and…

The point represented by 2+i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 22 units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by : 
  1. 1+i
  2. 2+2i
  3. -2-2i
  4. -1-i

Solution

Let P2+i   &  S(z)
By Rotation theorem, rotating about 3+3i, we get

z-3+3i3+i-3+3i=222e-iπ4

⇒ z-3-3i-2i=1-i

⇒ z-3-3i=-2i-2⇒ z=1+i

Asked in: JEE Main 2016 (09 Apr Online)

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