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If z1, z2, z3, z4 are the affixes of fou...

If `z_1, z_2, z_3, z_4` are the affixes of four point in the Argand plane, `z` is the affix of a point such that `|z-z_1|=|z-z_2|=|z-z_3|=|z-z_4|` , then prove that `z_1, z_2, z_3, z_4` are concyclic.

A

concylic

B

vertices of a triangle

C

vertices of a rhombus

D

in a straight line

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The correct Answer is:
a
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
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  2. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

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

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

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

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

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

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

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

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

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

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

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  13. Let z and omega be two non-zero complex numbers, such that |z|=|omega|...

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  14. If z ne 0 be a complex number and "arg"(z)=pi//4, then

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  15. (1+i)^8+(1-i)^8=?

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  16. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  17. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  18. For any complex number z, the minimum value of |z|+|z-1|

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  19. If (3pi)/(2) gt alpha gt 2 pi, find the modulus and argument of (1 -...

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  20. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Argand plane, then...

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