Home
Class 11
MATHS
Show that the area of the triangle on th...

Show that the area of the triangle on the Argand diagram formed by the complex numbers z, zi and `z+ zi` is `=(1)/(2) |z|^(2)`

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

Show that the area of the triangle on the Argand diagram formed by the complex number z ,i za n dz+i z is 1/2|z|^2

Show that the area of the triangle on the Argand diagram formed by the complex number z ,i za n dz+i z is 1/2|z|^2

Show that the area of the triangle on the Argand diagram formed by the complex number z ,i za n dz+i z is 1/2|z|^2

If the area of the triangle on the complex plane formed by complex numbers z, omegaz is 4 sqrt3 square units, then |z| is

If z is any complex number, then the area of the triangle formed by the complex number z, wz and z+wz as its sides, is

If the area of the triangle on the complex plane formed by the points z, iz and z+iz is 50 square units, then |z| is

If the area of the triangle on the complex plane formed by the points z, iz and z+iz is 50 square units, then |z| is

Find the circumstance of the triangle whose vertices are given by the complex numbers z_(1),z_(2) and z_(3) .

The area of the triangle formed by the points representing -z,iz and z-iz in the Argand plane, is

Let z_1,z_2,z_3 be three distinct non zero complex numbers which form an equilateral triangle in the Argand pland. Then the complex number associated with the circumcentre of the tirangle is (A) (z_1 z_2)/z_3 (B) (z_1z_3)/z_2 (C) (z_1+z_2)/z_3 (D) (z_1+z_2+z_3)/3

ICSE-COMPLEX NUMBERS-Chapter Test
  1. Show that the area of the triangle on the Argand diagram formed by the...

    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

    |