Home
Class 12
MATHS
If zk=cos((kpi)/10)+isin((kpi)/10), then...

If `z_k=cos((kpi)/10)+isin((kpi)/10)`, then `z_1z_2z_3z_4` is equal to

A

-1

B

2

C

-2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 1|55 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 2|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS )|22 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

If z_(k)=cos((k pi)/(10))+i sin((k pi)/(10)), then z_(1)z_(2)z_(3)z_(4) is equal to (A)-1 (B) 2(C)-2 (D) 1

If z= cos((8pi)/11)+isin((8pi)/11),i=sqrt(-1) then the value of Re(z+z^2+z^3+z^4+z^5) is lambda then 20lambda^2 =

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 then |z_(1)+z_(2)+z_(3)| is equal to

If |z_(1)|=1,|z_(2)|=2,|z_(3)|=3 and |9z_(1)z_(2)+4z_(1)z_(2)+z_(2)z_(3)|=12, then |z_(1)+z_(2)+z_(3)| is equal to

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE
  1. The number of complex numbers satisfying (1 + i)z = i|z|

    Text Solution

    |

  2. Suppose a, b, c in R and C lt 0. Let z = a + (b + ic)^(2015) + (b-ic)^...

    Text Solution

    |

  3. The number of solutions of z^(2) + |z| = 0 is

    Text Solution

    |

  4. The equation |((1+i)z-2)/((1+i)z+4)|=k does not represent a circle whe...

    Text Solution

    |

  5. If |z| ge 5, then least value of |z - (1)/(z)| is

    Text Solution

    |

  6. Principal argument of z = (i-1)/(i(1-"cos"(2pi)/(7))+"sin"(2pi)/(7)) i...

    Text Solution

    |

  7. If (x+iy) = sqrt((a+ib)/(c+id)) then prove that (x^2 + y^2)^2 = (a^2 ...

    Text Solution

    |

  8. For any three complex numbers z(1),z(2),z(3), if Delta=|{:(1,z(1),bar(...

    Text Solution

    |

  9. If x, y, a, b in R, a ne 0 and (a + ib) (x + iy) = (a^(2) + b^(2))i, t...

    Text Solution

    |

  10. If omega (ne 1) is a cube root of unity, then the value of tan[(omega^...

    Text Solution

    |

  11. If z is purely imaginary and Im (z) lt 0, then arg(i bar(z)) + arg(z) ...

    Text Solution

    |

  12. The inequality a + ib gt c + id is true when

    Text Solution

    |

  13. Let z in C be such that Re(z^(2)) = 0, then

    Text Solution

    |

  14. If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...

    Text Solution

    |

  15. If z = x + iy and 0 le sin^(-1) ((z-4)/(2i)) le (pi)/(2) then

    Text Solution

    |

  16. If a gt 0 and z|z| + az + 3i = 0, then z is

    Text Solution

    |

  17. If z is a complex numbers such that z ne 0 and "Re"(z)=0, then

    Text Solution

    |

  18. If zk=cos((kpi)/10)+isin((kpi)/10), then z1z2z3z4 is equal to

    Text Solution

    |

  19. If |z(1)| = |z(2)| = 1, z(1)z(2) ne -1 and z = (z(1) + z(2))/(1+z(1)z(...

    Text Solution

    |

  20. If z in C, then Re(bar(z)^(2))= k^(2), k gt 0, represents

    Text Solution

    |