Home
Class 11
MATHS
Let z1 and z2 be the nth roots of unity ...

Let `z_1` and `z_2` be the nth roots of unity which subtend a right angle at the origin then n must be the form

A

4k+1

B

4k+2

C

4k+3

D

4k

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos
  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

The locus of the midpoints of chords of the circle x^(2) + y^(2) = 1 which subtends a right angle at the origin is

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

z_(1) and z_(2) are two non-zero complex numbers, they form an equilateral triangle with the origin in the complex plane. Prove that z_(1)^(2)-z_(1)z_(2)+z_(2)^(2)=0

If alpha is the nth root of unity then 1+2alpha+3alpha^2+…. to n terms equal to

Let z_(1) and z_(2) be the roots of z ^(2)+az+b=0 . If the origin, z_(1) and z_(2) form an equilateral triangle. Then-

let z_1 and z_2 be roots of the equation z^2+pz+q=0 where the coefficients p and q may be complex numbers let A and B represnts z_1 and z_2 in the complex plane if angleAOB=alpha ne 0 and OA=OB where 0 is the origin prove that p^2=4qcos^2(alpha/2)

If z=omega,omega^2 where omega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex may be represented by a, z=1 b. z=0 c. z=-2 d. z=-1

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne+-1 consider an equilateral triangle inscribed in the circle with z_1,z_2,z_3 as the vertices taken in the counter clockwise directtion then z_1z_2z_3 is equal to

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If the fourth roots of unity are z1,z2,z3,z4 then z1^2+z2^2+z3^2+z4^2 ...

    Text Solution

    |

  2. If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is ...

    Text Solution

    |

  3. Let z1 and z2 be the nth roots of unity which subtend a right angle at...

    Text Solution

    |

  4. If x^5=(4-3i)^5 thrn the product of all of its roots (wheretheta=-tan^...

    Text Solution

    |

  5. If omega is an imaginary x^n root of unit then underset(r=1)oversetnsu...

    Text Solution

    |

  6. If omega(ne1) be a cube root of unity and (1+omega^2)^n=(1+omega^4)^n ...

    Text Solution

    |

  7. If absz=1 and z ne+-1 then all the values of z/(1-z^2) lie on

    Text Solution

    |

  8. If (1+2i)/(2+i)=r(costheta+isintheta) then

    Text Solution

    |

  9. If z1=a+ib and z2=c+id are two complex numbers lying on the circle x^...

    Text Solution

    |

  10. Number of solution(s) of the equation absz^2+7z=0 is/are

    Text Solution

    |

  11. If z1=9y^2-4-10ix,z2=8y^2-20i where z1=barz2 then z=x+iy is equal to

    Text Solution

    |

  12. Let z1,z2,z3 be three points on absz=1 let theta1,theta2 and theta3 be...

    Text Solution

    |

  13. If z1,z2 are two non zero complex numbers such that z1/z2+z2/z1=1 then...

    Text Solution

    |

  14. The complex numbers z1,z2 and z3 satisfying (z1-z3)/(z2-z3)=(1-isqrt3)...

    Text Solution

    |

  15. Let A(z1),A2(barz1) are the adjacent vertices of a regular polygon if ...

    Text Solution

    |

  16. If the points A(z),B(-z),C(1-z) are the vertices of an equilateral tri...

    Text Solution

    |

  17. Let z1 nez2 are two points in the Argand plane if a abs(z1)=b abs(z2) ...

    Text Solution

    |

  18. The least positive integer n for which ((1+i)/(1-i))^n=2/pisin^(-1)((1...

    Text Solution

    |

  19. If x=2+5i then the value of the expression x^3-5x^2+33x-49 is

    Text Solution

    |

  20. The square root of (1+i) is

    Text Solution

    |