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A particle P starts from the point z0=1+...

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`

A

6 + 7i

B

`- 7 +6i`

C

7 +6i

D

`- 6 +7i`

Text Solution

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The correct Answer is:
D
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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 (a)6+7i (b) -7+6i (c)7+6i (d) -6+7i

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ML KHANNA-COMPLEX NUMBERS -Problem Set (4) M.C.Q
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  2. If the area of the triangle on the complex plane formed by the points ...

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  3. If the area of the triangle on the complex plane formed by complex num...

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  4. The area of the triangle (in square units) whose vertices are i, omega...

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  5. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

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  6. If z(1)=1+2i, z(2)=2+3i, z(3)=3+4i, then z(1),z(2) and z(3) represent ...

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  7. If |z(1)|=|z(2)|=|z(3)| and z(1)+z(2)+z(3)=0, then z(1),z(2),z(3) are ...

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  8. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  9. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  10. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

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  11. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

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  12. If z(1),z(2) are vertices of an equilateral triangle with z(0) its cen...

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  13. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

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  14. If a and b are real numbers between 0 and 1 such that the points z(1...

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  15. The centre of a square is at the origin and 1 + i is one of its verti...

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  16. The points 1 + i, 1 - i, - 1 + i and - 1 - i are

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  17. If one vertex of a square whose diagonals intersect at the origin is 3...

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  18. If z(1) and overline(z)(1) represent adjacent vertices of a regular po...

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  19. A man walks a distance of 3 units from the origin towards the North...

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  20. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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