A particle P starts from the point z0=1+2 i, where i =√-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1 . From z1 the particle moves √2 units in the direction of the vector hati+ hatj and then it moves through an angle (π/2) in anticlockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by

Question

A particle P starts from the point z0=1+2 i, where i =√-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1 . From z1 the particle moves √2 units in the direction of the vector hati+ hatj and then it moves through an angle (π/2) in anticlockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by (A) 6+71 (B) -7+6 i (C) 7+6 i (D) -6+7 i

Tardigrade Admin · Accepted Answer

z 0 ≡(1+2 i ) z 1 ≡(6+5 i ) z 2 ≡(-6+7 i )

6+71

-7+6 i

7+6 i

-6+7 i

z0​≡(1+2i) z1​≡(6+5i) z2​≡(−6+7i)

$z_{0} \equiv (1 + 2 i)$
$z_{1} \equiv (6 + 5 i)$
$z_{2} \equiv (- 6 + 7 i)$