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The least distance between the circles |...

The least distance between the circles `|z|=12` and `|z-3-4i|=5` , is

A

0

B

2

C

7

D

17

Text Solution

Verified by Experts

The correct Answer is:
B
Let `z_(1)` be the affix of a point on `|z|=12` and `z_(2)` be that of on `|z-3-4i|=5`. Then,
`|z_(1)|=12` and `|z_(2)-3-4i|=5`
Now, `|z_(1)-z_(2)|=|z_(1)-(z_(2)-3-4i)-(3+4i)|`
`rArr |z_(1)-z_(2)| ge |z_(1)|-|z_(2)-3-4i|-|3+4i|`
`|z_(1)-z_(2)| le 12-5-5=2`
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
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  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

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  8. If cosA+cosB+cosC=0,sinA + sinB + sinC=0and A+B+C=180^0, then the valu...

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  9. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

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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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  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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

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  13. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

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  14. The centre of a square ABCD is at z0dot If A is z1 , then the centroid...

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

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

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  17. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

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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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