Home
Class 11
MATHS
For complex numbers u, v, one always has...

For complex numbers u, v, one always has :

A

`u^2+v^2 = |u|^2+ |v|^2`

B

`|u|+ |v|le |u+v|`

C

`|u-v| le |u|-|v|`

D

`|u+v| le |u|+|v|`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE|289 Videos

  • LIMITS AND DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|334 Videos

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise EXERCISE|85 Videos

Similar Questions

Explore conceptually related problems

If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c=(1-r)a+rb and w=(1 -r)u+rv,where r is a complex number, then the two triangles :

Represent the following complex numbers in the complex plane : i.

Represent the following complex numbers in the complex plane : 1 + 2i.

Represent the following complex numbers in the complex plane : 0+0i.

Represent the following complex numbers in the complex plane : 5- 7i.

Prove that for any complex number z, the product z bar(z) is always a non-negative real number.

Consider a quadratic equation az^2+bz+c=0, where a,b and c are complex numbers. The condition that the equation has one purely real root, is

Plot all the complex numbers in the complex number plane whose absolute value is 4.

Let C and R denote the set of all complex numbers and all real numbers respectively. Then show that f: C->R given by f(z)=|z| for all z in C is neither one-one nor onto.

A complex number U = 4+2i.The value of |U| is

MODERN PUBLICATION-LINEAR INEQUATIONS-EXERCISE
  1. The complex number z = x + iy, which satisfies the equation |(z-5i)/(z...

    Text Solution

    |

  2. In complex plane, the equation |z+ bar z|=|z- bar z| represents :

    Text Solution

    |

  3. For complex numbers u, v, one always has :

    Text Solution

    |

  4. If ((1+i)/(1-i))^n =1, then the smallest value of n is :

    Text Solution

    |

  5. Which of the following is correct ?

    Text Solution

    |

  6. In the Argand diagram. if O, P and Q represent respectively the origin...

    Text Solution

    |

  7. The area of the triangle with vertices affixed at z, iz, z(1 +i) is:

    Text Solution

    |

  8. Multiplication of a complex z by i corresponds to :

    Text Solution

    |

  9. If (c+i)/(c-i)= a+ ib, where a, b, c are real, then a^2+ b^2 equals :

    Text Solution

    |

  10. If i^2=-1, then the value of overset (200) underset (n=1) (sum) i^n is...

    Text Solution

    |

  11. If the conjugate of (x + iy) (1-2i) be 1+i, then :

    Text Solution

    |

  12. Mathematical Induction shows that the inequality log (n!) >n/2 holds :

    Text Solution

    |

  13. The inequality n ! > 2^(n-1) is true:

    Text Solution

    |

  14. The number of solutions of the equation z^2+ bar z=0 is :

    Text Solution

    |

  15. If alpha, beta are the roots fo the equation lamda(x^(2)-x)+x+55=0. If...

    Text Solution

    |

  16. The modulus of (1-i)/(3+i)+(4i)/5 is :

    Text Solution

    |

  17. For any complex number z, the minimum value of |z|+|z-1| is :

    Text Solution

    |

  18. If alpha, beta are the roots of x^2-a(x-1)+b=0, then the value of 1/(a...

    Text Solution

    |

  19. The sum of all real roots of the equation |x-2|^(2)+|x-2|-2=0 is

    Text Solution

    |

  20. The quadratic equation whose roots are three times the roots of 3ax^2 ...

    Text Solution

    |