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If A(z(1)) and A(z(2)) are two fixed poi...

If `A(z_(1))` and `A(z_(2))` are two fixed points in the Argand plane and a point P(z) moves in the Argand plane in such a way that `|z-z_(1)|=|z-z_(2)|`, then the locus of P, is

A

the line passing through A and B

B

the perpendicular bisector of the line segment joining A and B

C

a line passing through the mid-point of AB

D

a circle

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`|z-z_(1)|=|z-z_(2)|`
`rArr` PA=AB
`rArr` P moves in such a way that it is equidistant from A and B.
`rArr` Locus of P is the perpendicular bisector of the segment AB.
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
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  10. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

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  12. The expression (1+i)^(n1)+(1+i^(3))^(n(2)) is real iff

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  16. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

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  18. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

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  19. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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  20. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  21. The vertices of a square are z1,z2,z3 and z4 taken in the anticlockwis...

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