A particle P starts from the point `z_(0)=1+2i`, where `i=sqrt(-1)`. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units in the direction of the vector `hati+hatj` and then it moves through an angle `pi/2` in anticlockwise direction on a circle with center at origin, to reach a point `z_(2)`. The point `z_(2)` is given by

Options

A. `6+7i`
B. `-7+6i`
C. `7+6i`
D. `-6+7i`

Answer

D

Explanation

It is given that CE is the direction of vector `hati + hatj` which makes `45^(@)` with X-axis. Also, `CE=sqrt(2)`.

`therefore` CD=DE=1 unit
So, the coordinates of E are (7,6).
OE is rotated through an angle `pi/2` in anticlockwise direction to reach a point `F(z_(2))`.
`therefore z_(2) = bar(OE)e^(ipi//2)=(7+6i)i=-6+7i`