Home
Class 12
MATHS
If |z|=1, then the point representing th...

If `|z|=1,` then the point representing the complex number `-1+3z` will lie on a. a circle b. a parabola c.`` a straight line d. a hyperbola

A

a circle

B

a straight line

C

a parabola

D

a hyperbola

Text Solution

Verified by Experts

The correct Answer is:
A
`|z|=1," let "alpha=-1+3z`
`rArr alpha +1=3z`
`rArr |alpha+1|=3|z|=3`
Hence, `alpha` lies on a circle centered at `-1` and radius equal to 3.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWERS TYPE|49 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|36 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.11|6 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=2, the points representing the complex numbers -1+5z will lie on

if |z|=3 then the points representing thecomplex numbers -1+4z lie on a

If |z-1-i|=1 , then the locus of a point represented by the complex number 5(z-i)-6 is

Represent the complex numbers z= 1 + sqrt3i into polar form

Represent the complex number z = 1 +isqrt(3) in the polar form.

The points representing the complex numbers z for which |z+4|^(2)-|z-4|^(2)=8 lie on

The point representing the complex number z for which arg ((z-2)/(z+2))=pi/3 lies on

The points representing complex number z for which |z+2+ 3i| = 5 lie on the locus given by

If z ne 1 and (z^(2))/(z-1) is real, then the point represented by the complex number z lies

CENGAGE ENGLISH-COMPLEX NUMBERS-single correct Answer type
  1. If z=(i)^(i)^(((i)))w h e r e i=sqrt(-1),t h e n|z| is equal to 1 b. e...

    Text Solution

    |

  2. lf z = ilog(2-sqrt(3)), then cos z =

    Text Solution

    |

  3. If |z|=1, then the point representing the complex number -1+3z will li...

    Text Solution

    |

  4. The locus of point z satisfying R e(1/z)=k , where k is a non zero re...

    Text Solution

    |

  5. If z is complex number, then the locus of z satisfying the condition |...

    Text Solution

    |

  6. The greatest positive argument of complex number satisfying |z-4|=R e(...

    Text Solution

    |

  7. If ta n dc are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t...

    Text Solution

    |

  8. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

    Text Solution

    |

  9. Let C1 and C2 are concentric circles of radius 1and 8/3 respectively ...

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. If |z-1|lt=2a n d|omegaz-1-omega^2|=a (where omega is a cu...

    Text Solution

    |

  12. If |z^2-3|=3|z| , then the maximum value of |z| is 1 b. (3+sqrt(21))/2...

    Text Solution

    |

  13. If |2z-1|=|z-2|a n dz1, z2, z3 are complex numbers such that |z1-alpha...

    Text Solution

    |

  14. If z1 is a root of the equation a0z^n+a1z^(n-1)++a(n-1)z+an=3,w h e r ...

    Text Solution

    |

  15. If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqr...

    Text Solution

    |

  16. Let |Z(r) - r| le r, for all r = 1,2,3….,n. Then |sum(r=1)^(n)z(r)| is...

    Text Solution

    |

  17. All the roots of the equation 1 lz^(10) + 10iz^(9) + 10iz -11=0 lie

    Text Solution

    |

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

    Text Solution

    |

  19. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

    Text Solution

    |

  20. The roots of the cubic equation (z+ab)^3=a^3,a !=0 represents the ver...

    Text Solution

    |