Home
Class 11
MATHS
If arg((z-1)/(z+1)) = pi/2, show that x^...

If `arg((z-1)/(z+1))` = `pi/2`, show that `x^2+y^2-1=0`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |106 Videos

  • CONIC SECTION

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|90 Videos

Similar Questions

Explore conceptually related problems

If cos ^-1 x+cos ^(-1) y+cos ^(-1) z=pi and 0ltx, y ,zlt1 ,show that x^2+y^2+z^2+2 x y z=1

If (-1)ltx, y, z le 1 such that sin ^(-1) x+sin ^(-1) y+sin ^(-1) z=(3 pi)/2 , find the value of x^(2000)+y^(2001)+z^(2002)-(9/(x^(2000)+y^(2001)+z^(2002)))

If sin^(-1)x+sin^(-1)y+sin^(-1)z =(3pi)/2 , then find the value of x^2+y^2+z^2

If tan^-1x+tan^-1y+tan^-1z=pi ,show that x+y+z=xyz

If arg (bar(z)_(1))= "arg" (z_(2)), (z ne 0) then

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi/2 then the value of x^2+y^2+z^2+2xyz is equal to a)0 b)1 c)2 d)3

If sin^(-1)x+sin^(-1) y + sin ^(-1) z = (3pi)/2 , the value of x^(100)+y^(100)+z^(100) -9/(x^(101)+y^(101)+z^(101)) is : (i)0 (ii)1 (iii)2 (iv)3

The point of intersection of the straight line (x-2)/(2) = (y-1)/(-3) = (z+2)/(1) with the plane x+3y - z + 1=0 is a) (3,-1,1) b) (-5,1,-1) c) (2,0,3) d) (4,-2,-1)

A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. If the points P,Q,R,S are representing the complex numbers -1, 3i, 3+2...

    Text Solution

    |

  2. If z = x+iy, prove that arg(z -1) = tan^(-1)(y/(x-1)) and arg(z+1) = t...

    Text Solution

    |

  3. If arg((z-1)/(z+1)) = pi/2, show that x^2+y^2-1=0

    Text Solution

    |

  4. Express sqrt3-i in polar form using the polar form of sqrt3+i

    Text Solution

    |

  5. Use De-Moivere's theorem to find (sqrt3-i)^9 and (sqrt3-i)^(-1) in rec...

    Text Solution

    |

  6. Determine also, for which values of nepsilonZ, (sqrt3-i)^n is real

    Text Solution

    |

  7. Express 1 + i in modulus amplitude form

    Text Solution

    |

  8. Prove that (1 + i)^4 = -4

    Text Solution

    |

  9. Represent the complex number 1+sqrt3i in the polar form.

    Text Solution

    |

  10. What is the polar form of 1 - sqrt3i?

    Text Solution

    |

  11. Prove that (1 + sqrt3i)^n + (1 - sqrt3i)^n = 2^(n+1) cos ((npi)/3) for...

    Text Solution

    |

  12. Solve : x^2 - 2x + 4 = 0

    Text Solution

    |

  13. If alpha and beta are the roots of x^2 - 2x + 4 = 0, Prove that alpha^...

    Text Solution

    |

  14. Express (1+i)/sqrt3+i in the form x + iy. Hence, find the polar form o...

    Text Solution

    |

  15. Nisha derived the polar form of (1+i)/sqrt3+i by using the polar forms...

    Text Solution

    |

  16. Using the polar form and x + iy form of (1+i)/sqrt3+i, prove that cosp...

    Text Solution

    |

  17. Fill in the blank by choosing the correct answer from the bracket. If ...

    Text Solution

    |

  18. Suppose alpha and beta are two complex numbers so that absbeta = 1. Ra...

    Text Solution

    |

  19. Match the following

    Text Solution

    |

  20. Express the following in a+ib form. (1-i)^4

    Text Solution

    |