Home
Class 11
MATHS
If z=3/(2+costheta+isintheta) then show ...

If `z=3/(2+costheta+isintheta)` then show that z lies on a circle in the complex plane

A

a straight line

B

a circle having centre on y axis

C

a parabola

D

a circle having centre on x axis

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos
  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

If x+iy=2/(3+costheta+isintheta) ,show that 2x^2+2y^2=3x-1

Let P denotes a complex number z=r(costheta+isintheta) on the Argand's plane, and Q denotes a complex number sqrt(2|z|^(2))(cos(theta+(pi)/(4))+isin(theta+(pi)/(4))) . If 'O' is the origin, then DeltaOPQ is

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of the point representing in the complex plane.

If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex plane is a circle.

If z=x+iyand(z-i)/(z+1) is purely imaginary, then show that the point z always lies on a circle.

If z=x+iy and |z-1|^(2)+|z+1|^(2)=4, determine the position of the point z in the complex plane.

z_(1) and z_(2) are two non-zero complex numbers such that z_(1)^(2)+z_(1)z_(2)+z_(2)^(2)=0 . Prove that the ponts z_(1),z_(2) and the origin form an isosceles triangle in the complex plane.

Find the complex number omega satisfying the equation z^3=8i and lying in the second quadrant on the complex plane.

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. if log(1/2)(( absz^2+2absz+4)/(2absz^2+1))lt0 then the region traced b...

    Text Solution

    |

  2. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

    Text Solution

    |

  3. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  4. If z=iloge(2-sqrt3) then the value of cosz

    Text Solution

    |

  5. If alpha is the nth root of unity then 1+2alpha+3alpha^2+….to n terms ...

    Text Solution

    |

  6. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  7. If alpha=cos((8pi)/11+isin((8pi)/11 then Re(alpha+alpha^2+alpha^3+alph...

    Text Solution

    |

  8. If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus ...

    Text Solution

    |

  9. x^(3m)+x^(3n-1)+x^(3r-2) where m,n,r in N is divisible by

    Text Solution

    |

  10. A fourth root of -1 is

    Text Solution

    |

  11. If z1=a+ib and z2=c+id are complex numbers such that abs(z1)=abs(z2)=1...

    Text Solution

    |

  12. Let z1 and z2 be complex numbers such that z1 nez2 and absz1=absz2 if ...

    Text Solution

    |

  13. If (x+2)^3-27=0 then a value of x is

    Text Solution

    |

  14. If absomega=1 then the set of points z=omega+1/omega is contained in o...

    Text Solution

    |

  15. If z1 lies on absz=1 and z2 lies on absz=2 then

    Text Solution

    |

  16. IfA(z1),B(z2),C(z3) and D(z4) be the vertices of the square ABCD then

    Text Solution

    |

  17. If z1 and z2 are non zero complex numbers such that abs(z1-z2)=absz1+a...

    Text Solution

    |

  18. The reflection of the complex number (2-i)/(3+i) where (i=sqrt(-1)in t...

    Text Solution

    |

  19. If alpha is a complex constant such that alphaz^2+z+baralpha=0 has are...

    Text Solution

    |

  20. Let A,B,C b ethree sets of complex numbers as defined A={z:Im zge 1} ...

    Text Solution

    |