Home
Class 12
MATHS
If z=x+iy, where i=sqrt(-1), then the eq...

If z=x+iy, where `i=sqrt(-1)`, then the equation `abs(((2z-i)/(z+1)))=m` represents a circle, then m can be

A

`1//2`

B

1

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`|(2z-i)/(z+1)|=m rArr |z-i/2|=m/2|z+1|`
This shows that the given equation will represent a circle, if `m/2 ne 1`, i.e., `m ne 2`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|141 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|15 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

Similar Questions

Explore conceptually related problems

If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a circle, when m is (a) 1/2 (b). 1 (c). 2 (d). 3

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

The equation |z-1|=|z+1|,i= sqrt(-1) represents =

The equation |z-i|=|x-1|, i=sqrt(-1) , represents :

If x=3i, y=2i, z=m+I, and i=sqrt(-1) , then the expression xy^(2)z=

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

If z = x + iy, x , y in R , then the louts Im (( z - 2 ) /(z + i)) = (1 ) /(2) represents : ( where i= sqrt ( - 1))

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these

OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
  1. If z=x+iy, where i=sqrt(-1), then the equation abs(((2z-i)/(z+1)))=m r...

    Text Solution

    |

  2. The locus of the center of a circle which touches the circles |z-z1|=a...

    Text Solution

    |

  3. Prove that for positive integers n(1) and n(2), the value of express...

    Text Solution

    |

  4. The value of abs(sqrt( 2i) - sqrt(2i)) is :

    Text Solution

    |

  5. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  6. The value of ((1+ i sqrt(3))/(1-isqrt(3)))+ ((1-isqrt(3))/(1+isqrt(3)...

    Text Solution

    |

  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

    Text Solution

    |

  8. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

    Text Solution

    |

  9. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

    Text Solution

    |

  10. The value of the expression (1+(1)/(omega))+(1+(1)/(omega^(2)))+(2+(1)...

    Text Solution

    |

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

    Text Solution

    |

  12. The expression (1+i)^(n1)+(1+i^(3))^(n2) is real iff

    Text Solution

    |

  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

    Text Solution

    |

  14. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

  15. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

    Text Solution

    |

  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |