Home
Class 12
MATHS
1+ i = sqrt(2) ( cos "" (pi)/( 4) + i si...

` 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) `
`1 + omega + omega^(2) = 0, omega = e^((2 pi i)/3)`
`( 1+ x)^(n) = P_(0) + P_(1) x + P_(2) x^(2) + P_(3) x^(3) + P_(4) x ^(4) + . . . + P_(n) x^(n)`
`p_(1) + p_(4) + p_(7) + . . . = (1)/(3) [2^(n) + 2 cos ( n - 2) (pi)/(3)]`. True or False?

Text Solution

Verified by Experts

The correct Answer is:
3S
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (2) (True and False )|4 Videos

  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (2) (Fill in the blanks)|2 Videos

  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (1) (True and False)|5 Videos

  • CO-ORDINATE GEOMETRY OF THREE DIMENSION

    ML KHANNA|Exercise SELF ASSIGNMENT TEST |11 Videos

  • CONCEPTS OF SET THEORY

    ML KHANNA|Exercise Self Assessment Test|13 Videos

Similar Questions

Explore conceptually related problems

If omega = "cos"(pi)/(n) + "i sin" (pi)/(n) , then value of 1 + omega + omega^(2) +...+omega^(n-1) is

if (1+x)^(n)=p_(0)+p_(1)x+p_(2)x^(2)+--+p_(n)x^(n) the value of p_(1)-p_(3)+p_(5)+...

If (1+x)^(n)=p_(0)+p_(1)x+p_(2)x^(2)+....+p_(n)x^(n) then (p_(0)-p_(2)+p_(4)-p_(6)+....)/(p_(1)-p_(3)+p_(5)-p_(7)+......)=

If (1-x+x^(2))^(4)=1+P_(1)x+P_(2)x^(2)+P_(3)x^(3)+...+P_(8)x^(8) , then prove that : P_(2)+P_(4)+P_(6)+P_(8)=40 and P_(1)+P_(3)+P_(5)+P_(7)=-40 .

ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If x^(2) - 2 x cos theta + 1 = 0 " then " x^(2 n) - 2 x ^(n) cos n th...

    Text Solution

    |

  2. The following in the form A + i B ( cos 2 theta + i sin 2 theta )^(-...

    Text Solution

    |

  3. If x = cos theta + i sin theta , y = cos phi + i sin phi z = cos Ps...

    Text Solution

    |

  4. If a = cos alpha + i sin alpha , b = cos beta + i sin beta , " then ...

    Text Solution

    |

  5. If cos A + cos B + cos C = 0, sin A + sin B + sin C = 0 and A + B +...

    Text Solution

    |

  6. If cos A + cos B + cos C = 0 = sin A + sin B + sin C , then

    Text Solution

    |

  7. The general value of x which satisfies the equation ( cos x + i sin ...

    Text Solution

    |

  8. Find the theta such that (3+2i sin theta)/(1-2 isin theta) is (a) re...

    Text Solution

    |

  9. If ( tan theta - i [ sin ( theta // 2) + cos ( theta // 2) ])/( 1 + 2...

    Text Solution

    |

  10. Let f(p) ( beta) = ( cos "" (beta)/( p^(2)) + i sin "" (beta)/( p^(2)...

    Text Solution

    |

  11. The continued product of the four values of [ cos (pi/ 3) + i sin (...

    Text Solution

    |

  12. If a = cos alpha + i sin alpha, b = cos beta + i sin beta , " then " ...

    Text Solution

    |

  13. If alpha , beta be the roots of the the equation x^(2) - 2 x + 2 =...

    Text Solution

    |

  14. The complex number z has argZ = theta ,0 lt theta lt (pi)/(2) and sat...

    Text Solution

    |

  15. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

    Text Solution

    |

  16. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

    Text Solution

    |

  17. 1 + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega...

    Text Solution

    |

  18. 1 + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega...

    Text Solution

    |

  19. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

    Text Solution

    |

  20. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1+ omega ...

    Text Solution

    |