Home
Class 12
MATHS
If omega = z//[z-(1//3)i] and |omega| = ...

If `omega = z//[z-(1//3)i] and |omega| = 1`, then find the locus of z.

A

a straight line

B

a parabola

C

an ellipse

D

a circle

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 7|11 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

If w= z/(z-i1/3) and |w|=1,then z lies on:

Let z and omega be complex numbers. If Re(z) = |z-2| , Re(omega) = |omega - z| and arg(z - omega) = pi/3 , then the value of Im(z+w) , is

If |z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)+z_(2)z_(3)|= 12 , then find the value of |z_(1) + z_(2) + z_(3)| .

If |z_(1) -1|le,|z_(2) -2| le2,|z_(3) - 3|le 3, then find the greatest value of |z_(1) + z_(2) + z_(3)|

If |z| <= 1 and |omega| <= 1, show that |z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- bar w z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 (c) z=bar z (d) None of these

1. If |z-2+i| ≤ 2 then find the greatest and least value of | z|

If arg (z^(1//2))=(1)/(2)arg(z^(2)+barzz^(1//3)), find the value of |z|.

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .

If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If z1a n dz2 are two nonzero complex numbers such that |z1+z2|=|z1|+|z...

    Text Solution

    |

  2. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

    Text Solution

    |

  3. If omega = z//[z-(1//3)i] and |omega| = 1, then find the locus of z.

    Text Solution

    |

  4. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

    Text Solution

    |

  5. Find the value of sum(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wher...

    Text Solution

    |

  6. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

    Text Solution

    |

  7. A man walks a distance of 3 units from the origin towards the North-...

    Text Solution

    |

  8. If |z|=1 and z!=1, then all the values of z/(1-z^2) lie on

    Text Solution

    |

  9. If abs(z+4) le 3, the maximum value of abs(z+1) is

    Text Solution

    |

  10. Let A, B, C be three sets of complex number as defined below: A={z:Img...

    Text Solution

    |

  11. What is 5% Equals to

    Text Solution

    |

  12. Express in the form of complex number i^9+i^(19)

    Text Solution

    |

  13. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

    Text Solution

    |

  14. If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...

    Text Solution

    |

  15. Let z = x + iy be a complex number where x and y are integers. Then...

    Text Solution

    |

  16. Let z=costheta+isintheta. Then the value of sum(m-&gt;1-15)Img(z^(2m-1...

    Text Solution

    |

  17. If |z-4/z|=2 then the greatest value of |z| is:

    Text Solution

    |

  18. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

    Text Solution

    |

  19. Find the value of 2^4

    Text Solution

    |

  20. If alpha and beta are the roots of the equation x^2"-"x""+""1""=""0 , ...

    Text Solution

    |