Home
Class 12
MATHS
Let z=x+iy and omega=(1-iz)/(z-i). If |o...

Let z=x+iy and `omega=(1-iz)/(z-i).` If `|omega|=1` show the in the complex plane the point z lies on the real axis.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVEEXAMS(Multiple Corrrect Answer type)|7 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise EXERCISE 4(SHORT ANSWER TYPE QUESTION )|58 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (E. Assertion-Reason Type)|2 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

The area of the triangle in the complex plane formed by the points z, iz and z+iz is

Find the complex number z=e^(i(pi)) in the form x+iy .

If arg ((z-1)/(z+1))=pi/4 ,, then show that in complex plane, the locus of z is a cricle.

If z=x+iyandw=(1-iz)/(z-i) such that |w|=1 , then show that z is purely real.

If z=x+iy and w=(1-iz)/(1+iz) such that |w|=1.then show that z is purely real.

If absomega=1 then the set of points z=omega+1/omega is contained in or equal to

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

If z=x+iy and (z-i)/(z+1) is purely imaginary,then show that the point z always lies on a circle.

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

If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
  1. If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))...

    Text Solution

    |

  2. If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-...

    Text Solution

    |

  3. If y=sqrt(x^(2)+6x+8), show that one value of sqrt(1+iy)+sqrt(1-iy)[i...

    Text Solution

    |

  4. Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

    Text Solution

    |

  5. prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc...

    Text Solution

    |

  6. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  7. Express each of the following expressions as the sum of two squares: ...

    Text Solution

    |

  8. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  9. If a,b are real and a^(2)+b^(2)=1 then show that the equation (sqrt(1...

    Text Solution

    |

  10. If z=x+iy and |z|=1, show that (z-1)/(z+1)(z!=-1) is a purely imaginar...

    Text Solution

    |

  11. If z(1)and z(2) be any two non-zero complex numbers such that |z(1)+z(...

    Text Solution

    |

  12. If alpha be the real positive cube root and beta,gamma be the complex ...

    Text Solution

    |

  13. If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex ...

    Text Solution

    |

  14. In the complex plane, the vertices of an equlitateral triangle are rep...

    Text Solution

    |

  15. Show that the area of the triangle on the Argrand Diagram formed by th...

    Text Solution

    |

  16. If z(1)^(2)+z(2)^(2)+z(3)^(2)-z(1)z(3)-z(1)z(2)-z(2)z(3)=0" ""prove th...

    Text Solution

    |

  17. Solve bar(z)=iz^(2) (z being a complex number)

    Text Solution

    |

  18. Solve : |z|+z=2+i (z being a complex number)

    Text Solution

    |

  19. If z=x+iy then show that |x|+|y|lesqrt2|x+iy|.

    Text Solution

    |

  20. Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the comple...

    Text Solution

    |