Home
Class 12
MATHS
Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1...

Let `z=(-1+sqrt(3)i)/(2)`, where `i=sqrt(-1)`, and `r, s in {1, 2, 3}`. Let `P=[((-z)^(r),z^(2s)),(z^(2s),z^(r))]` and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which `P^(2)=-I` is ______.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|92 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

let z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let P= [((-z)^r, z^(2s)),(z^(2s), z^r)] and I be the idenfity matrix or order 2. Then the total number of ordered pairs (r,s) or which P^2=-I is

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

If z = (sqrt(3+i))/2 (where i = sqrt(-1) ) then (z^101 + i^103)^105 is equal to

If z(2-2sqrt(3i))^2=i(sqrt(3)+i)^4, then a r g(z)=

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

Let z=9+ai, where i=sqrt(-1) and a be non-zero real. If Im(z^(2))=Im(z^(3)) , sum of the digits of a^(2) is

If z = 3 -2i then the value s of (Rez) (Im z)^(2) is

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is

If p=(sqrt(q)+z)/(r^(2)+z) , what is the value of z in terms of p, q, and r ?

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lam...

    Text Solution

    |

  2. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  3. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

    Text Solution

    |

  4. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  5. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

    Text Solution

    |

  6. Let P be a matrix of order 3xx3 such that all the entries in P a...

    Text Solution

    |

  7. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  11. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  12. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  13. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

    Text Solution

    |

  14. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

    Text Solution

    |

  15. Let a,b,c be real numbers with a^(2) +b^(2) +c^(2)=1. Then show tha...

    Text Solution

    |

  16. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

    Text Solution

    |

  17. Suppose f(x) is a function satisfying the following conditions: f(0)=...

    Text Solution

    |

  18. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  19. Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...

    Text Solution

    |

  20. For all values of A ,B ,Ca n dP ,Q ,R show that |"cos"(A-P)"cos"(A-Q)"...

    Text Solution

    |