Home
Class 12
MATHS
If |z(1)|=|z(2)|=1, then prove that [{:(...

If `|z_(1)|=|z_(2)|=1`, then prove that `[{:(,z_(1),-z_(2)),(,bar(z)_(2),bar(z)_(1)):}] [{:(,bar(z)_(1),z_(2)),(,-bar(z)_(2),z_(1)):}]=[{:(,1//2,0),(,0,1//2):}]`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-II:|28 Videos
  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos
  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If z_(1)= 3 + 5i and z_(2)= 2- 3i , then verify that bar(((z_(1))/(z_(2))))= (bar(z)_(1))/(bar(z)_(2))

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

For two unimobular complex numbers z_(1) and z_(2) , find [(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]^(-1)

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)-z_(2)| gt |z_(1)|-|z_(2)|

If z_(1) = 3+ 2i and z_(2) = 2-i then verify that (i) bar(z_(1) + z_(2)) = barz_(1) + barz_(2)

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)z_(2)|= |z_(1)||z_(2)|

If z_(1)=2-i, z_(2)=1+ 2i, then find the value of the following : (i) Re((z_(1)*z_(2))/(bar(z)_(2))) (ii) Im (z_(1)*bar(z)_(2))

If |z_(1)|= |z_(2)|= ….= |z_(n)|=1 , prove that |z_(1) + z_(2) + …+ z_(n)|= |(1)/(z_(1)) + (1)/(z_(2)) + …(1)/(z_(n))|

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

RESONANCE ENGLISH-MATRICES & DETERMINANT-HLP
  1. If a,b,c are real number, and D=|{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+...

    Text Solution

    |

  2. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

    Text Solution

    |

  3. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

    Text Solution

    |

  4. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

    Text Solution

    |

  5. Let A be a (4xx4) matrix such that the sum of elements in each row is ...

    Text Solution

    |

  6. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

    Text Solution

    |

  7. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

    Text Solution

    |

  8. Let p and q be real number such that x^(2)+px+q ne0 for every real num...

    Text Solution

    |

  9. Let A,B,C be three 3 xx 3 matrices with real enteries. If BA+BC+AC=1, ...

    Text Solution

    |

  10. If |z(1)|=|z(2)|=1, then prove that [{:(,z(1),-z(2)),(,bar(z)(2),bar(z...

    Text Solution

    |

  11. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. If the system of equations x=cy+bz, y=az+cx and z=bx+ay has non-trivia...

    Text Solution

    |

  14. IfD=d i ag[d1, d2, dn] , then prove that f(D)=d i ag[f(d1),f(d2), ,f(...

    Text Solution

    |

  15. Fiven the matrix A= [[-1,3,5],[1,-3,-5],[-1,3,5]] and X be the solut...

    Text Solution

    |

  16. If q is a characteristic root of an singular matrix A, then prove that...

    Text Solution

    |

  17. Show that if lambda(1), lambda(2), ...., lambda(n) are n eigenvalues o...

    Text Solution

    |

  18. If there an three square matrices A, B, C of same order satisying th...

    Text Solution

    |

  19. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

    Text Solution

    |

  20. If a rank is a number associated with a matrix which is the highest or...

    Text Solution

    |