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The centre of a square ABCD is at z=0, A...

The centre of a square ABCD is at z=0, A is `z_(1)`. Then, the centroid of `/_\ABC` is (where, `i=sqrt(-1)`)

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 ENGLISH-COMPLEX NUMBERS -Exercise
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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 equation |(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 the complex number z(1) " and " z(2) are such that arg (z(1)) - ar...

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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 z(1),z(2),z(3),z(4) are the affixes of the four points in the Ar...

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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=1,2,3,…n

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  14. If z(1),z(2) and z(3), z(4) are two pairs of conjugate complex numbers...

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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+dot+logz^n=0i s

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  18. If |z(1)|= |z(2)|= ….= |z(n)|=1, prove that |z(1) + z(2) + …+ z(n)|= |...

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  20. If omega(!=1) is a cube root of unity, then value of the determinant|1...

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