Home
Class 11
MATHS
If z be a non-zero complex number, show ...

If z be a non-zero complex number, show that `(bar(z^(-1)))= (bar(z))^(-1)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (A)|27 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (B)|69 Videos

  • COMPLEX NUMBER

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |34 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

Similar Questions

Explore conceptually related problems

If z and w are two non-zero complex numbers such that z=-w.

If z is a non -zero complex number then (|barz|^(2))/(zbarz) is equal to

Let z_(1) and z_(2) be two non -zero complex number such that |z_(1)+z_(2)| = |z_(1) | = |z_(2)| . Then (z_(1))/(z_(2)) can be equal to ( omega is imaginary cube root of unity).

If z is a non zero complex, number then |(|barz |^2)/(z barz )| is equal to (a). |(barz )/z| (b). |z| (c). |barz| (d). none of these

If z_1 and z_2 are two complex numbers such that (z_1-2z_2)/(2-z_1bar(z_2)) is unimodular whereas z_1 is not unimodular then |z_1| =

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

Let z and omega be two non-zero complex numbers, such that |z|=|omega| and "arg"(z)+"arg"(omega)=pi . Then, z equals

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot

ICSE-COMPLEX NUMBERS-Chapter Test
  1. If z be a non-zero complex number, show that (bar(z^(-1)))= (bar(z))^(...

    Text Solution

    |

  2. Find the square root of 5-12i

    Text Solution

    |

  3. Find the locus of a complex number z=x +yi, satisfying the relation |z...

    Text Solution

    |

  4. Express (13i)/(2-3i) in the form A + Bi

    Text Solution

    |

  5. If z= x +yi and (|z-1-i|+4)/(3|z-1-i|-2)=1, show that x^(2) + y^(2) -2...

    Text Solution

    |

  6. If omega and omega^(2) are cube roots of unity, prove that (2- omega +...

    Text Solution

    |

  7. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

    Text Solution

    |

  8. If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of ...

    Text Solution

    |

  9. Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

    Text Solution

    |

  10. Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

    Text Solution

    |

  11. Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + i...

    Text Solution

    |

  12. Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

    Text Solution

    |

  13. Find the locus of a complex number z= x + yi, satisfying the relation ...

    Text Solution

    |

  14. Find the real values of x and y satisfying the equality (x-2 + (y-3)i)...

    Text Solution

    |

  15. If i= (sqrt-1), prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)...

    Text Solution

    |

  16. If z= x + yi and |2z + 1| = |z- 2i|, show that 3(x^(2) + y^(2)) + 4(x-...

    Text Solution

    |

  17. Find the amplitude of the complex number "sin" (6pi)/(5) + i (1- "cos"...

    Text Solution

    |

  18. Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

    Text Solution

    |

  19. Find the value of x and y given that (x + yi) (2-3i)=4+i

    Text Solution

    |

  20. If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z l...

    Text Solution

    |

  21. If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and...

    Text Solution

    |