A particle P starts from the point Z₀=1+2 i where i= -1 . It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive y -axis by 3 units to reach a point Z₁ . From Z₁ the particle moves 2 units in the direction of vector i + j and then it moves through an angle 2 in anticlockwise direction on a circle with centre at origin to reach at point Z₂ , then Z₂=

Step-by-step solution

The particle starts at Z₀ = 1+2i . Moving horizontally away from the origin increases the real component by 5 units, yielding 6+2i . Vertical movement upward then adds 3 to the imaginary part: 6+5i . Next, displacement in the direction of i + j corresponds to adding the complex number 1+i , giving 7+6i . A rotation of 2 anticlockwise about the origin multiplies by i : (7+6i)i = -6+7i . The final position is Z₂ = -6+7i .