Home
Class 11
MATHS
If z + 1/z = 2costheta, prove that |(z^...

If `z +` 1/z ` = 2costheta,` prove that `|(z^(2n)-1)//(z^(2n)+1)|=|tanntheta|`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

If |z|=1 and z'=(1+z^(2))/(z) , then

If Z_1 = -3 + 4i , Z_2 = 12 - 5i , prove that |z_1+z_2|<|z_1-z_2|

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)

Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then prove that |z|=1.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. a ,b , c are integers, not all simultaneously equal, and omega is cube...

    Text Solution

    |

  2. a, b, c are reals such that a+b+c=3 and   1/(a+b)+ 1/(b+c) + 1/ (c+...

    Text Solution

    |

  3. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

    Text Solution

    |

  4. If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , ...

    Text Solution

    |

  5. The locus represented by the equation abs(z-1)=abs(z-i) is

    Text Solution

    |

  6. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

    Text Solution

    |

  7. If a ,b ,c are non-zero real numbers, then find the minimum value of t...

    Text Solution

    |

  8. If z1a n dz2 are two nonzero complex numbers such that =|z1+z2|=|z1|+|...

    Text Solution

    |

  9. If diagonals of a parallelogram bisect each other, prove that its a rh...

    Text Solution

    |

  10. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

    Text Solution

    |

  11. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

    Text Solution

    |

  12. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  13. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

    Text Solution

    |

  14. Referred to the principal axes as the axes of co ordinates find the eq...

    Text Solution

    |

  15. Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot

    Text Solution

    |

  16. Find sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

    Text Solution

    |

  17. If the equation a x^2+b x+c=0(a &gt;0) has two real roots alphaa n db...

    Text Solution

    |

  18. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<...

    Text Solution

    |

  19. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

    Text Solution

    |

  20. Let z=x+i y be a complex number, where xa n dy are real numbers. Let...

    Text Solution

    |