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The center of a square ABCD is at z=0. T...

The center of a square ABCD is at z=0. The affix of the vertex A is `z_(1)`. Then, the affix of the centroid of the triangle ABC is

A

`z_(1)(cospi+-isinpi)`

B

`z_(1)/3(cospi+-sinpi)`

C

`z_(1)(cos(pi/2)+-sin(pi/2))`

D

`z_(1)/3(cos(pi/2)+-sin(pi/2))`

Text Solution

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The correct Answer is:
d
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The product of all values of (cosalpha+isinalpha)^(3//5) is

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  2. If C^(2)+S^(2)=1, then (1+C+iS)/(1+C-iS) is equal to

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  3. The center of a square ABCD is at z=0. The affix of the vertex A is z(...

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  4. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

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  5. The vector z=-4+5i is turned counter clockwise through an angle of 180...

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  6. The value of [sqrt(2)(cos(56^(@)15^('))+isin(56^(@)15^('))]^(8), is

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  7. Find the complex number z satisfying the equations |(z-12)/(z-8i)|=5/...

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  8. The vertices B and D of a parallelogram are 1-2i and 4-2i If the diago...

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  9. If for complex numbers z(1) and z(2), arg z(1)-"arg"(z(2))=0 then |z(1...

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  10. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

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  11. If z1, z2, z3, z4 are the affixes of four point in the Argand plane, z...

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  12. The value of sum(r=1)^(8)(sin(2rpi)/9+icos(2rpi)/9), is

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  13. If z(1),z(2),z(3),…………..,z(n) are n nth roots of unity, then for k=1,2...

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  14. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers then arg...

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  15. If |z(1)|=|z(2)| and arg (z(1))+"arg"(z(2))=0, then

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

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  17. The value of z satisfying the equation logz+logz^(2)+……..+logz^(n)=0...

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  18. If |z(1)|=|z(2)|=………….=|z-(n)|=1, then the value of |z(1)+z(2)+………+z(n...

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  19. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

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  20. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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