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

Options

A. `2+2i`
B. `-2-2i`
C. `1+i`
D. `-1-i`

Answer

C

Explanation

Let P(2,1) be the point representing `(2+i)` and Q be its position when it moves 1 unit eastward. The coordinates of Q are (3,1). Let R(3,3) be the position when point moves 2 units northwards. Let S be the final position of the point, such that RS `=2sqrt(2)`.

`bar(RS)=(RS)/(RQ)bar(RQ)e^(ipi//4)`
`rArr z-(3+3i) =(2sqrt(2))/(2)[(3+i)-(3+3i)]e^(-ipi//4)`
`rArr z-(3+3i)=-2sqrt(2)i(1/sqrt(2)-1/sqrt(2)i)`
`rArr z=1+i`