Home
Class 12
MATHS
Let z in c be such that |z| lt . If omeg...

Let `z in c` be such that `|z| lt `. If `omega = (5 + 3z)/(5(1 - z))`, then ,

A

` 5 Re (omega) gt 4 `

B

`4 Im (omega) gt 5 `

C

`5 Re (omega) gt 1 `

D

`5 Im (omega) lt 1`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

Let z in C be such that |z| lt 1 .If omega =(5+3z)/(5(1-z) then

Let z and omega be complex numbers such that |z|=|omega| and arg (z) dentoe the principal of z. Statement-1: If argz+ arg omega=pi , then z=-baromega Statement -2: |z|=|omega| implies arg z-arg baromega=pi , then z=-baromega

Find the locus of z if omega= (z)/(z- (1)/(3)i), |omega| =1

Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 and |z-iomega|=|z-i bar omega|=2, then z equals (a) 1ori (b). ior-i (c). 1or-1 (d). ior-1

Let z be a complex number such that |(z-5i)/(z+5i)|=1 , then show that z is purely real

If z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z_1, z_2 , z_3 in C such that |z_1 | = |z_2| = |z_3| = |z_1+ z_2+ z _3| = 4 . If |z_1 - z _2 | = | z _1 + z _ 3 | and z_2 ne z_3 , then values of |z_1 + z_2 |* |z_1 + z _ 3| is _____.

If z satisfies |z-1| lt |z +3| " then " omega = 2 z + 3 -i satisfies

Let z_1=6+i and z_2=4-3i . If z is a complex number such thar arg ((z-z_1)/(z_2-z))= pi/2 then (A) |z-(5-i)=sqrt(5) (B) |z-(5+i)=sqrt(5) (C) |z-(5-i)|=5 (D) |z-(5+i)|=5

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

    Text Solution

    |

  2. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

    Text Solution

    |

  5. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

    Text Solution

    |

  6. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

    Text Solution

    |

  7. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

    Text Solution

    |

  8. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

    Text Solution

    |

  9. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

    Text Solution

    |

  10. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

    Text Solution

    |

  11. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

    Text Solution

    |

  12. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

    Text Solution

    |

  13. Let z in c be such that |z| lt . If omega = (5 + 3z)/(5(1 - z)), then ...

    Text Solution

    |

  14. If z = ((1+i)^(2))/(alpha-i), alpha in R has magnitude sqrt((2)/(5)) ...

    Text Solution

    |

  15. Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=p...

    Text Solution

    |

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

    Text Solution

    |

  17. if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

    Text Solution

    |

  18. if z is a complex number belonging to the set S={z:|z-2+i|gesqrt(5)} a...

    Text Solution

    |

  19. Let alpha and beta are roots of equation x^(2)-x-1=0 with alpha > bet...

    Text Solution

    |

  20. If omega is a cube root of unity but not equal to 1, then minimum valu...

    Text Solution

    |