A particle starts from a point `z_0=1+i` where `i=sqrt(-1)`. lt moves horizontally away from origin by 2 units and then vertically away from origin by 3 units to reach a point `z_1`, From `z_1` particle moves `sqrt5` units in the direction of `2hat i+3hatj` and then it moves through àn angle of `cosec^(-1) 2` in anticlockwise direction of a circle with centre at origin to reach a point `z_2`. The arg `z_1` is given by

Options

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

Answer

D

Explanation

`z_2= (6 + sqrt(2) cos 45 ^@, 5 + sqrt(2)sin 45 ^@)` = (7,6)= 7 + 6i By rotaion about (0,0)
`(z_2)/(z_2) =e^(I pi//2) rArr z_2 = z_2 (e^(ipi/2))`
`=(7 + 6i ) (cos ""pi/2+ i sin ""(pi)/2)=(7+ 6i )(i)=-6+ 7i `