Home
Class 12
MATHS
Let z(1) and z(2) be n^(th ) roots of un...

Let `z_(1)` and `z_(2)` be `n^(th )` roots of unity which subtend a right angle at the origin. Then n must be of the form.

A

4 k+1

B

4 k+2

C

4 k+3

D

4 k

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMMON ENTRANCE TEST -2016

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos
  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

Similar Questions

Explore conceptually related problems

The locus of the mid-points of chords of the circle x^2+y^2 =4 , which subtend a right angle at the origin, is:

Let AB be a chord of the circle x^2+y^2=a^2 subtending a right angle at the centre. Then the locus of the centroid of triangle PAB as P moves on the circle is:

Let z_(1) and z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number, assume that the origin z_(1) and z_(2) form an equilateral triangle , then

The locus of the midpoint of a chord of the circle x^(2)+y^(2) = 4 which subtends a right angle at the origin is

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Complex numbers z_(1),z_(2)andz_(3) are the vertices A,B,C respectivelt of an isosceles right angled triangle with right angle at C. show that (z_(1)-z_(2))^(2)=2(z_1-z_(3))(z_(3)-z_(2)).

If P_x,P_y and P_z are the magnitudes of forces on a body actin mutually at right angles to each other, then represent the resultant force on the body in (1) a scaler and (2) vector form.

If z_(1),z_(2)and z_(3) are the vertices of an equilateral triangle with z_0 as its circumcentre , then changing origin to z_0 ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.

Let z_(1) and z_(2) be two distinct complex numbers and let z=(1-t)z_(1)+tz_(2) for some real number t with 0 lt t lt 1 . If Arg (w) denotes the principal argument of a non zero complex number w , then

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365)=

    Text Solution

    |

  2. If z(1),z(2),z(3) are complex numbers such that : |z(1)|=|z(2)|=|z(3)|...

    Text Solution

    |

  3. Let z(1) and z(2) be n^(th ) roots of unity which subtend a right angl...

    Text Solution

    |

  4. Let omega=-(1)/(2)+i (sqrt(3))/(2), then the value of |[1,1,1],[1,-...

    Text Solution

    |

  5. The complex numbers z(1), z(2), z(3) satisfying (z(1)-z(3))/(z(2)-z(3)...

    Text Solution

    |

  6. For all complex numbers z(1), z(2) satisfying |z(1)|=12 and |z(2)-3-...

    Text Solution

    |

  7. If z is a complex number such that |z|=1, z ne 1, then the real part o...

    Text Solution

    |

  8. If omega be a cube root of unity and (1+omega^(2))^(n)=(1+omega^(4))^(...

    Text Solution

    |

  9. If |z|=1 and z ne pm 1, then all the values of (z)/(1-z^(2)) lie on

    Text Solution

    |

  10. The value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqr...

    Text Solution

    |

  11. If alpha+ibeta=tan^(-1)z, z=x+iy and alpha is constant, then locus of ...

    Text Solution

    |

  12. The value of (i)^(i) is

    Text Solution

    |

  13. In the Argand diagram all the complex numbers z satisfying |z-4 i|+|z+...

    Text Solution

    |

  14. The equation |z+1-i|=|z-1+i| represents a

    Text Solution

    |

  15. If z is any complex number satisfying |z-1|=1, then which of the follo...

    Text Solution

    |

  16. If the amplitude of z-2-3 i is (pi)/(4), then the locus of z=x+i y is

    Text Solution

    |

  17. If omega is a non real cube root of unity then (a+b)(a+b omega)(a+b om...

    Text Solution

    |

  18. If sqrt(a+i b)=x+i y, then a possible value of sqrt(a-i b) is

    Text Solution

    |

  19. If i^(2)=-1 then i+i^(2)+i^(3)+…..... . upto 1000 terms is equal to

    Text Solution

    |

  20. If omega is a complex cube root of unity then the value of (p++q omega...

    Text Solution

    |