Home
Class 11
MATHS
Prove that the locus of midpoint of line...

Prove that the locus of midpoint of line segment intercepted between real and imaginary axes by the line `a z + a z+b=0,w h e r eb` is a real parameterand `a` is a fixed complex number with nondzero real and imaginary parts, is `a z+ a z =0.`

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

For the real parameter t,the locus of the complex number z=(1-t^2)+isqrt(1+t^2) in the complex plane is

The locus of point z satisfying Re(1/z)=k , where k is a non-zero real number is

Prove that the equation Z^3+i Z-1=0 has no real roots.

If z ne 1 and (z^2)/(z-1) is real then the point represented by the complex number z lies

Let z, omega be complex numbers such that barz+ibaromega=0 and arg(z omega)=pi , then arg z equals

Show that the equation of a circle passing through the origin and having intercepts a and b on real and imaginary axes, respectively, on the argand plane is given by z bar z =a(R e z)+b(I mz)dot

If zne1and(z^(2))/(z-1) is real , then the point represented by the complex number z lies -

If Z is a non-real complex number, then find the minimum value of | (Imz^5)/(Im^5z) |

Let z=9+b i ,and b is nonzero real and i^2=-1. If the imaginary part of z^2a n dz^3 are equal, then b/3 is ______.

If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of the point representing in the complex plane.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

    Text Solution

    |

  2. If x= (7+4sqrt(3)), prove that x+1//x= 14

    Text Solution

    |

  3. Prove that the locus of midpoint of line segment intercepted between ...

    Text Solution

    |

  4. Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.

    Text Solution

    |

  5. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

    Text Solution

    |

  6. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

    Text Solution

    |

  7. If alpha=(z-i)/(z+i), show that, when z lies above the real axis, alph...

    Text Solution

    |

  8. Solve 4^x+6^x=9^xdot

    Text Solution

    |

  9. Let x1, x2 are the roots of the quadratic equation x^2+a x+b=0,w h e r...

    Text Solution

    |

  10. Solve 3^(2x^2-7x+7)=9.

    Text Solution

    |

  11. Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in ...

    Text Solution

    |

  12. How many solutions does the equation(8^x + 27^x)/(12^x +18^x) = 7/6hav...

    Text Solution

    |

  13. Is the following computation correct? If not give the correct compu...

    Text Solution

    |

  14. Consider an equilateral triangle having verticals at point A(2/sqrt3 e...

    Text Solution

    |

  15. Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=...

    Text Solution

    |

  16. Find the value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i...

    Text Solution

    |

  17. Let z,z(0) be two complex numbers. It is given that abs(z)=1 and the n...

    Text Solution

    |

  18. Show that the equation a z^3+b z^2+ barb z+ bara =0 has a root alpha ...

    Text Solution

    |

  19. If nge3and1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are the n,nth ...

    Text Solution

    |

  20. Find the maximum and minimum values of the function y=(log)e(3x^4-2x^3...

    Text Solution

    |