Home
Class 11
MATHS
Let z be a complex number satisfying equ...

Let `z` be a complex number satisfying equation `z^p-z^(-q)=0,\ where\ p ,q in N ,\t h e n` (A) if `p=q` , then number of solutions of equation will be infinite. (B) if `p=q` , then number of solutions of equation will be finite. (C) if `p!=q` , then number of solutions of equation will be `p+q+1.` (D) if `p!=q` , then number of solutions of equation will be `p+qdot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

Let p,qin N and q gt p , the number of solutions of the equation q|sin theta |=p|cos theta| in the interval [0,2pi] is

If p ,q , in {1,2,3,4}, then find the number of equations of the form p x^2+q x+1=0 having real roots.

If p ,q , in {1,2,3,4}, then find the number of equations of the form p x^2+q x+1=0 having real roots.

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

For a complex number z, the equation z^(2)+(p+iq)z+ r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2)-1 ), then

Find p, where p,q belongs to R If p and q are the roots of equation x^2-px+q=0 then p=,

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If center of a regular hexagon is at the origin and one of the vertice...

    Text Solution

    |

  2. Let a ,b , c be the sides of a triangle, where a!=b!=c and lambda in...

    Text Solution

    |

  3. Let z be a complex number satisfying equation z^p-z^(-q)=0,\ where\ p ...

    Text Solution

    |

  4. Let S be the set of all non-zero real numbers such that the quadratic ...

    Text Solution

    |

  5. A complex number z is rotated in anticlockwise direction by an angle ...

    Text Solution

    |

  6. For real x, the function ((x-a)(x-b))/(x-c) will assume all real value...

    Text Solution

    |

  7. If z1, z2 are two complex numbers (z1!=z2) satisfying |z1^2-z2^2|=| z...

    Text Solution

    |

  8. The quadratic equation p(x)=0 with real coefficients has purely imagi...

    Text Solution

    |

  9. If from a point P representing the complex number z1 on the curve |z...

    Text Solution

    |

  10. Let alpha and beta be the roots x^2-6x-2=0, with alpha > beta If an=al...

    Text Solution

    |

  11. If |z-3|=min{|z-1|,|z-5|}, then Re(z) equals to

    Text Solution

    |

  12. For the following question, choose the correct answer from the codes ...

    Text Solution

    |

  13. Minimum value of| z1- z2| as z1& z2 over the curves √3

    Text Solution

    |

  14. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  15. If p=a+bomega+comega^2, q=b+comega+aomega^2, and r=c+aomega+bomega^2,...

    Text Solution

    |

  16. If the roots of the quadratic equation (4p-p^2-5)x^2-(2p-1)x+3p=0 lie ...

    Text Solution

    |

  17. If z1=5+12 i and |z2|=4,t h e n

    Text Solution

    |

  18. If roots of x^2-(a-3)x+a=0 are such that at least one of them is great...

    Text Solution

    |

  19. If |z-1|-1,t h e n a r g((z-1-i)//z) can be equal to pi//4 (z-2)//z ...

    Text Solution

    |

  20. Let f(x)=a x^2+bx +c a ,b ,c in R. If f(x) takes real values for re...

    Text Solution

    |