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Question

A particle P starts from the point z0=1+2i, where i=1. It moves first horizontally away from the origin by 3 units to reach a point z1. From z1 the particle moves 2 units in the direction of the vector i + j anf then it moves through an angle π/2 in anticlockwise direction on a circle with center at the origin to reach a point z2. Then point z2 is given by

A
6+7i
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B
7+6i
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C
7+6i
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D
3+5i
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Solution

The correct option is D 3+5i
The particle P starts from the point z0=1+2i.
It reaches point z1
z1=z0+(3+0i)=1+2i+3=4+2i
From z1 the particle moves 2 units in the direction of the vector i+j.

Position of particle =4+2i+2(cosπ4+isinπ4)
=4+2i+1+i=5+3i
From there particle moves through an angle π2 in anticlockwise direction on a circle with center at the origin to reach z2.
z2=(5+3i)(cosπ2+isinπ2)
z2=(5+3i)i=3+5i
z2=3+5i

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