Home
Class 11
MATHS
Let complex numbers alpha and 1/alpha^-...

Let complex numbers `alpha` and `1/alpha^-` lie on circles `(x-x_0)^2+(y-y_0)^2=r^2` and `(x-x_0)^2+(y-y_0)^2=4r^2` respectively if `z_0=x_0+iy_0` satisfies the equation `2absz_0^2=r^2+2` then `absalpha=`

A

`1/sqrt2`

B

(1/2)

C

`1/sqrt7`

D

(1/3)

Text Solution

Verified by Experts

The correct Answer is:
C
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

Let complex numbers alphaand (1)/(alpha) lie on circles (x-x_(0))^(2)+(y-y_(0))^(2)=r^(2)and(x-x_(0))^(2)+(y-y_(0))^(2)=4r^(2) respectively . If z_(0)=x_(0)+iy_(0) satisfies the equation 2|z_(0)|^(2)=r^(2)+2 " then "|alpha| =

The number of common tangents to the circles x^2+y^2-4x-6y-12=0 and x^2+y^2+6x+18y+26=0

The number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0 is :

If the circle x ^(2) +y^(2) -4rx- 2ry+4r^(2)=0 and x^(2) +y^(2) =25 touch each other, then r satisfies-

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

The circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect at an angle of

If (a,0) is a point on a diameter of the circle x^2+y^2=4 , then x^2-4x-a^2=0 has

Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is -

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

  2. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

    Text Solution

    |

  3. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

    Text Solution

    |

  4. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

    Text Solution

    |

  5. If z is a complex number of unit modulus and argument theta then arg(...

    Text Solution

    |

  6. Let z1=2+3i and z2=3+4i be two points on the complex plane then the se...

    Text Solution

    |

  7. Suppose z=x+iy where x and y are real numbers and i=sqrt(-1) the point...

    Text Solution

    |

  8. If P,Q,R are angles of an isosceles triangle and anglep=pi/2 then the ...

    Text Solution

    |

  9. Let z be a complex number such that the imaginary part of z is non zer...

    Text Solution

    |

  10. If z ne 1 and (z^2)/(z-1) is real then the point represented by the co...

    Text Solution

    |

  11. The maximum value of absz when the complex number z satisfies the cond...

    Text Solution

    |

  12. If (3/2+isqrt3/2)^50=3^25(x+iy)where x and y are real then the order P...

    Text Solution

    |

  13. If (z-1)/(z+1) is purely imaginary then

    Text Solution

    |

  14. The points representing the complex number z for which arg((z-2)/(z+2)...

    Text Solution

    |

  15. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  16. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |

  17. If omega(ne1) is a cube root of unity and (1+omega)^7=A+Bomega then (A...

    Text Solution

    |

  18. For the real parameter t,the locus of the complex number z=(1-t^2)+isq...

    Text Solution

    |

  19. If x+(1/x)=2costheta then for any integer n,x^n+1/x^n=

    Text Solution

    |

  20. If omega ne1 is a cube root of unity then the sum of the series S=1+2o...

    Text Solution

    |