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 to reach a point `z_1dot` From `z_1` the particle moves `sqrt(2)` units in the direction of the vector ` hat i+ hat j` and then it moves through an angle `pi/2` in anticlockwise direction on a circle with centre at origin, to reach a point `z_2dot` The point `z_2` is given by `6+7i` (b) `-7+6i` `7+6i` (d) `-6+7i`

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`