Home
Class 12
MATHS
If 1,alpha,alpha^(2),………..,alpha^(n-1) a...

If `1,alpha,alpha^(2),………..,alpha^(n-1)` are the n, `n^(th)` roots of unity and `z_(1)` and `z_(2)` are any two complex numbers such that `sum_(r=0)^(n-1)|z_(1)+alpha^(R ) z_(2)|^(2)=lambda(|z_(1)|^(2)+|z_(2)|^(2))`, then `lambda=`

A

n

B

`(n-1)`

C

`(n+1)`

D

2n

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|15 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

Similar Questions

Explore conceptually related problems

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

If z_(-)1 and z_(-)2 are any two complex numbers show that |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2|z_(1)|^(2)+2|z_(2)|^(2)

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

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

If omega is the 2014^("th") root of unity and z_(1) and z_(2) be any two complex numbers such that |z_(1)|=3,|z_(2)|=4 then value of underset(k=0)overset(2013)sum |z_(1)+omega^(k)z_(2)|^(2) is

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then probe that . Sigma_(n-1)^(k=0)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

Let alpha be the non-real 5 th root of unity. If z_1 and z_2 are two complex numbers lying on |z| = 2 , then the value of sum_(t=0) ^(4) |z_1 + alpha ^(t)z_2 |^(2) is ______ .

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

    Text Solution

    |

  2. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

    Text Solution

    |

  3. If alpha,beta,gamma and delta are the equation x^(4)-1 = 0, then the v...

    Text Solution

    |

  4. If omega is a complex cube root of unity, then the equation |z- omega|...

    Text Solution

    |

  5. If omega is a complex cube root of unity, then the equation |z- omega|...

    Text Solution

    |

  6. The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radiu...

    Text Solution

    |

  7. z is such that a r g ((z-3sqrt(3))/(z+3sqrt(3)))=pi/3 then locus z is

    Text Solution

    |

  8. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

    Text Solution

    |

  9. If |z-4+3i| leq 1 and m and n be the least and greatest values of |z...

    Text Solution

    |

  10. If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unit...

    Text Solution

    |

  11. If z(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0...

    Text Solution

    |

  12. The least positive integer n for which ((1+i)/(1-i))^n= 2/pi sin^-1 (...

    Text Solution

    |

  13. The area of the triangle formed by the points representing -z,iz and z...

    Text Solution

    |

  14. If z(0)=(1-i)/2, then the value of the product (1+z(0))(1+z(0)^(2))(1+...

    Text Solution

    |

  15. The greatest positive argument of complex number satisfying |z-4|=R e(...

    Text Solution

    |

  16. If the points in the complex plane satisfy the equations log(5)(|z|+3)...

    Text Solution

    |

  17. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

    Text Solution

    |

  18. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

    Text Solution

    |

  19. If z(1) and z(2) satisfy the equation 2|z+3|=|"Re"(z)| and arg(z+3)/(1...

    Text Solution

    |

  20. If A=|z in C: z=x+ix-1 for all x in R} and |z| le |omega| for all z, o...

    Text Solution

    |