Home
Class 11
MATHS
If z(1), z(2) in C (set of complex numbe...

If `z_(1), z_(2) in C` (set of complex numbers), prove that `|z_(1) + z_(2)| le |z_(1)| + |z_(2)|`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (F )|28 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

State true or false for the following. Let z_(1) " and " z_(2) be two complex numbers such that |z_(2) + z_(2)| = |z_(1) | + |z_(2)| , then arg (z_(1) - z_(2)) = 0

Statement-1, if z_(1) and z_(2) are two complex numbers such that |z_(1)| le 1, |z_(2)| le 1 , then |z_(1)-z_(2)|^(2) le (|z_(1)|-|z_(2)|)^(2)-"arg"(z_(2))}^(2) Statement-2 sintheta gt theta for all theta gt 0 .

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

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

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

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

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

ICSE-COMPLEX NUMBERS-Chapter Test
  1. If z= x +yi and (|z-1-i|+4)/(3|z-1-i|-2)=1, show that x^(2) + y^(2) -2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If 1, omega, omega^(2) are the three cube roots of unity, then simplif...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the modulus and argument of the complex number (2 + i)/(4i + (1+ ...

    Text Solution

    |