Home
Class 11
MATHS
If omega is the cube root of unity then ...

If `omega` is the cube root of unity then `cos[(omega^200+1/omega^200)pi+pi/4]` equals

A

`-1/sqrt2`

B

`+1/sqrt2`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
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

If omega is the complex cube root of unity, then find omega+1/omega

If omega is the complex cube root of unity, then find omega^22+1/omega^22

If omega is the complex cube root of unity, then find (1+omega^2)(1+omega^4)

If omega is the complex cube root of unity, then find (1-omega^2)(1-omega^4)

If omega is the complex cube root of unity, then find 1/omega^405

If omega is the complex cube root of unity, then find (1-omega+omega^2)^4

If omega is the complex cube root of unity, then find (1+omega-omega^2)^3

If omega is the complex cube root of unity, then find (2-omega+2omega^2)^4

If omega is the complex cube root of unity, then find (2+omega+omega^2)^3

If omega is the complex cube root of unity, then find (2+omega+omega^2)^5

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If A(z1), B(z2), C(z3) are the vertices of an equilateral triangle ABC...

    Text Solution

    |

  2. If 1, omega,omega^2 are the three cube roots of unity, then (1-omega+o...

    Text Solution

    |

  3. If omega is the cube root of unity then cos[(omega^200+1/omega^200)pi+...

    Text Solution

    |

  4. If omega is a complex cube root of unity and (1+omega)^7=A+Bomega then...

    Text Solution

    |

  5. the area of the triangle formed by 1, omega, omega^2 where omega be th...

    Text Solution

    |

  6. The value of i^100+i^101+i^102+i^103

    Text Solution

    |

  7. If argzlt0, then arg(-z)-argz is equal to

    Text Solution

    |

  8. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then ar...

    Text Solution

    |

  9. The common roots of the equations z^3+2z^2+2z+1=0 and z^1985+z^100+1=0...

    Text Solution

    |

  10. abs(z-6)ltabs(z-2) its solution is given by

    Text Solution

    |

  11. If abs(z^2-1)=absz^2+1, then z lies on

    Text Solution

    |

  12. If xr=cos(pi/2^r)+isin(pi/2^r) then x1x2x3.......infty=

    Text Solution

    |

  13. The value of [(1+cos(pi/8)+isin(pi/8))/(1+cos(pi/8)-isin(pi/8))]^8 is

    Text Solution

    |

  14. The area of the triangle in the complex plane formed by the points z, ...

    Text Solution

    |

  15. The origin and the roots of the equation z^2+pz+q=0 form an equilatera...

    Text Solution

    |

  16. If n is a positive integer, then, (1+isqrt3)^n+(1-isqrt3)^n=

    Text Solution

    |

  17. If absz1=absz2=absz3=1 and z1+z2+z3=0, then z1, z2, z3 are vertices of

    Text Solution

    |

  18. The locus of point z satisfying Re(1/z)=k, where k is a non-zero real ...

    Text Solution

    |

  19. If P represents z=x+iy in the argand plane and abs(z+1-i)=abs(z+i-1) t...

    Text Solution

    |

  20. If alpha/a+beta/b+gamma/c=1+i and a/alpha+b/beta+c/gamma=0, then the v...

    Text Solution

    |