Home
Class 12
MATHS
If z=1+3i then show that z, iz and z+zi ...

If `z=1+3i` then show that `z`, `iz` and `z+zi` form a right angled isosceles triangle.

Text Solution

Verified by Experts

The correct Answer is:
`BC=AC`and `AB^(2)=BC^(2)+AC^(2)` we see that the triangle is right angled isosceles triangle.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.1|6 Videos

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.2|9 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

Similar Questions

Explore conceptually related problems

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If acosA=bcosBthen show that the triangle is either an isosceles triangle or right angled triangle.

If z_1^2+z_2^2+2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

Given the complex number z = 3 + 2i , represent the complex number z, iz and z + iz in one Argand diagram. Show that these complex numbers form the veritices of an isosceles right triangle .

If z_1, z_2, z_3 be the affixes of the vertices A, B Mand C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + Z_2 + Z_3 =

If |z|=1 show that 4 le |z+4-3i| le 6 .

If |z| = 1, show that 2 le |z^(3) - 3| le 4.

If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to

If z= re^(i theta)" then "|e^(iz)|=

PREMIERS PUBLISHERS-COMPLEX NUMBERS-Problem for practice
  1. If z=1+3i then show that z, iz and z+zi form a right angled isosceles ...

    Text Solution

    |

  2. If (1-i)/(1+i) is a root of the equation ax^(2)+bx+1=0. Where a, b...

    Text Solution

    |

  3. If is a cubeth root of unity root of : (1-omega+omega^(2))^(4)+(1+om...

    Text Solution

    |

  4. The arguments of the roots of a complex number differ by :

    Text Solution

    |

  5. If z(1)=4+5i and z(2)=-3+2i that (z(1))/(z(2)) is :

    Text Solution

    |

  6. The number of values of (costheta+isintheta)^(p//q) where p and q are ...

    Text Solution

    |

  7. If -i+3 is a root of x^(2)-6x+k=0. Then the value of k is :

    Text Solution

    |

  8. If x^(2)+y^(2)=1, then the value of (1+x+iy)/(1+x-iy).

    Text Solution

    |

  9. The value of ((-1 + isqrt3)/(2))^(100) + ((-1-isqrt3)/(2))^(100) is :

    Text Solution

    |

  10. The principal value of arg(z) lies in the interval :

    Text Solution

    |

  11. If -barz lies in the third quadrant then z lies in the :

    Text Solution

    |

  12. If P is ((1)/(2)+i(sqrt(3))/(2)) and OP is rotated through an angle (p...

    Text Solution

    |

  13. If the amplitude of a complex number is (pi)/(2) then the number is :

    Text Solution

    |

  14. If A+iB=(a(1)+ib(1))(a(2)+ib(2))(a(3)+ib(3)) then A^(2)+B^(2) is :

    Text Solution

    |

  15. The points z(1)z(2)z(3)z(4) in the complex plane are the vertices of a...

    Text Solution

    |

  16. If omega is the cube root of unity, then then value of (1 - omega) (1 ...

    Text Solution

    |

  17. Find the correct statement : The cube roots of unity are :

    Text Solution

    |

  18. Which of the following is incorrect.?

    Text Solution

    |

  19. Which of the following is incorrect ?

    Text Solution

    |

  20. Which of the following is incorrect ?

    Text Solution

    |

  21. Which of the following is correct statement ?

    Text Solution

    |