Home
Class 12
MATHS
If omega is a complex number such that |...

If `omega` is a complex number such that `|omega|=r!=1` , and `z=omega+1/omega` , then locus of `z` is a conic. The distance between the foci of conic is 2 (b) `2(sqrt(2)-1)` (c) 3 (d) 4

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If omega is any complex number such that z omega=|z|^(2) and |z-barz|+|omega+baromega|=4 , then as omega varies, then the area bounded by the locus of z is

If z and omega are two non-zero complex numbers such that |zomega|=1 and arg(z)-arg(omega)=pi/2 , then barzomega is equal to

Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=pi//2 then

If z and w are two non-zero complex numbers such that z=-w.

If z and w are two complex number such that |z w|=1 and a rg(z)-a rg(w)=pi/2 , then show that barz w=-i

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

If z and w are two complex number such that |zw|=1 and arg (z) – arg (w) = pi/2, then show that overline zw = -i.

If za n dw are two complex number such that |z w|=1a n da rg(z)-a rg(w)=pi/2 , then show that z w=-idot

If z is a complex number satisfying the equation |z-(1+i)|^2=2 and omega=2/z , then the locus traced by 'omega' in the complex plane is

If z is a complex number satisfying the equation |z-(1+i)|^2=2 and omega=2/z , then the locus traced by 'omega' in the complex plane is

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If z1a n dz2 are two complex numbers satisfying |z-4|=R e(z) and havin...

    Text Solution

    |

  2. The number solution of the equation sgn(x^2)=|x-2| is 1 (b) 0 (c) 2...

    Text Solution

    |

  3. If omega is a complex number such that |omega|=r!=1 , and z=omega+1/om...

    Text Solution

    |

  4. The equation 2log(x+3)=log(alphax) has only one solution if

    Text Solution

    |

  5. If 4^(sin2x+2cos^(2)x)+4^(1-sin2x+2sin^(2)x)=65 ,then(sin2x+cos2x) has...

    Text Solution

    |

  6. If x^2+2a x+a<0AAx in [1,2], the find the values of a.

    Text Solution

    |

  7. The solution of the differential equation 2x^2y(dy)/(dx)=tan(x^2y^2)-2...

    Text Solution

    |

  8. If (x^2-7|x|+10)/(x^2-6x+9)<0 then x can belongs to a(-5,-2) b.(2,3...

    Text Solution

    |

  9. (lim)(xvecoo)((a x+3)/(b x+2))^(bx) is equal to ( a and b are positive...

    Text Solution

    |

  10. If alpha=cos ((2pi)/5)+isin((2pi)/5) , then find the value of alpha+al...

    Text Solution

    |

  11. The graphs of y=sin x ,y=cos x , y=t a n x& y=cos e c x drawn on the s...

    Text Solution

    |

  12. Evaluate ("lim")(xvec0)((sinx)/x)^(((sinx)/(x-sinx)))

    Text Solution

    |

  13. If m and n are the smallest positive integers satisfying the relations...

    Text Solution

    |

  14. If tan25^(@)=a, then the value of (tan205^(@)-tan115^(@))/(tan245^(@)+...

    Text Solution

    |

  15. Let f(x) is a continuous function symmetric about the lines x=1a n dx...

    Text Solution

    |

  16. If cos x=- (1)/(3) and x lies in Quadrant III find the values ...

    Text Solution

    |

  17. If int (x^9+x^6+x^3)(2x^6+3x^3+6)^(1/3) dx=1/a(2x^9+3x^6+6x^3)^(4/3)+c...

    Text Solution

    |

  18. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  19. Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)...

    Text Solution

    |

  20. Draw the region bounded by x^2 + y^2 >1 and x^2/1+y^2/4 le 1

    Text Solution

    |