Home
Class 12
MATHS
Let omega be a complex cube root of unit...

Let `omega` be a complex cube root of unity with `omegane1` and `P = [p_ij]` be a n × n matrix with ` p_(ij) = omega^(i+j)` . Then `P^2ne0,` , when n =

A

57

B

55

C

58

D

56

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

Let omega be a complex cube root of unity with omega ne 0 and P=[p_(ij)] be an n x n matrix with p_(ij)=omega^(i+j) . Then p^2ne0 when n is equal to :

Let omega be a complex cube root of unity with omega!=1 and P=[p_(ij)] be a n xx n matrix withe p_(ij)=omega^(i+j). Then p^(2)!=O, when n=a..57b 55c.58d.56

If omega ne 1 is a cube root of unity, then 1, omega, omega^(2)

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4 .

Let omega ne 1 be a complex cube root of unity. If ( 4 + 5 omega + 6 omega ^(2)) ^(n^(2) + 2) + ( 6 + 5omega^(2) + 4 omega ) ^(n ^(2) + 2) + ( 5+ 6 omega + 4 omega ^(2) ) ^( n ^(2) + 2 ) = 0 , and n in N , where n in [1, 100] , then number of values of n is _______.

If omega!=1 is the complex cube root of unity and matrix H=[[omega,00,omega]], then H^(70) is equal to

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Match the statement in Column I with those in Column II. [Note : He...

    Text Solution

    |

  2. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

    Text Solution

    |

  3. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  4. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  5. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  6. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  7. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |

  8. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  9. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

    Text Solution

    |

  10. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

    Text Solution

    |

  11. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

    Text Solution

    |

  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  14. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

    Text Solution

    |

  15. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  16. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

    Text Solution

    |

  17. Let P=[{:((-z)^r,z^(2r)),(z^(2r),z^r):}] and Ibe the identity matrix o...

    Text Solution

    |

  18. Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the co...

    Text Solution

    |

  19. Let s ,\ t ,\ r be non-zero complex numbers and L be the set of ...

    Text Solution

    |

  20. For a non-zero complex number z , let arg(z) denote the principal ar...

    Text Solution

    |