Home
Class 11
MATHS
Show that (x+yw+zw^2)^2+(xw^2+y+zw)^2+(x...

Show that `(x+yw+zw^2)^2+(xw^2+y+zw)^2+(xw+yw^2+z)^2=0`,where w is an cube (imaginary ) root of 1.

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 15

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

  • MODEL QUESTION PAPERS-SET 3

    UNITED BOOK HOUSE|Exercise EXERCISE|48 Videos

Similar Questions

Explore conceptually related problems

If z^2+abs(z)^2=0 then find the imaginary value of z

Show x^5-2x^2+7 =0 has atleast two imaginary roots.

If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then show that xyz=a^(3)+b^(3) "where " omega is a complex cube root of 1 . Find square root of - 2i.

If p lt 0 and alpha, beta, gamma are cube roots of p then for any a,b and c show that (aalpha+b beta + cgamma)/(a beta+bgamma +calpha)=omega^(2) where omega is an imaginary cube root of 1.

(b) answer any one of the foll.: (i) prove without expanding |[1,omega,omega ^2],[omega ,omega ^2 ,1],[omega ^2,1, omega]|=0 wher w is an imaginary cube root of unity.

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an imaginary cube root of unity.

If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where omega is a imaginary cube root of unity)

Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=k has no imaginary root, where A,B,C....H and a,b,c....,and Kin R.

Evalute: |{:(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1):}| , where omega is an imaginary cube root of unity .

Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where omega is an imaginary cube root of unity ).

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 2-EXERCISE
  1. Find the maximum value of 1/2sin^2theta+1/3cos^2theta

    Text Solution

    |

  2. Show that tan8alpha-tan5alpha-tan3alpha=tan8alphatan5alphatan3alpha

    Text Solution

    |

  3. Show that (x+yw+zw^2)^2+(xw^2+y+zw)^2+(xw+yw^2+z)^2=0,where w is an cu...

    Text Solution

    |

  4. What is the permutations of the letters in the word CAMBRIDGE when M,R...

    Text Solution

    |

  5. Which term of the expansion of (2x^2-x^-1)^12is the term independent o...

    Text Solution

    |

  6. Find the least value of a when a+b=4 and 2a+3ble25

    Text Solution

    |

  7. Find the perpendicular distance from (2,3,4) to x- axis and z- axis.

    Text Solution

    |

  8. Convert the straight line sqrt3x+y+14=0 into normal form.

    Text Solution

    |

  9. Evaluate :lim(xrarra)(root(3)(x)-root(3)(a))/(x-a)

    Text Solution

    |

  10. IS the derivative of the function f(x)=|x| at x=0.possible?

    Text Solution

    |

  11. In a frequancy distribution,if the mean = 35 & median = 33, then find ...

    Text Solution

    |

  12. A box contains 6 white balls and 4 black balls, A ball is drawn at ran...

    Text Solution

    |

  13. In three sets P,Q,R if Pcup R=Pcup Qand Pcap Q=PcapR,then show that Q=...

    Text Solution

    |

  14. Show that,tan7 (1^@/2)=sqrt6-sqrt3+sqrt2-2

    Text Solution

    |

  15. Prove by mathematical induction, n.1+(n-1).2+(n-2).3+…+2.(n-1)+1.n = ...

    Text Solution

    |

  16. If a+ib=sqrt((x+iy)/(p+iq)),show that (a^2+b^2)^2=(x^2+y^2)/(p^2+q^2)

    Text Solution

    |

  17. If the p^(th), q^(th) and r^(th) terms of a G.P. are x, y, z respec...

    Text Solution

    |

  18. The co-efficients of the expansion of (1+x)^(2n-1)and (1+x)^(2n)are P ...

    Text Solution

    |

  19. The co-ordinates of the vertices of a quadrilateral are (3,-2)(6,2)(4,...

    Text Solution

    |

  20. Find the equations of straight line which are perpendicular to the str...

    Text Solution

    |