Home
Class 12
MATHS
Prove that ((i+sqrt3)/2)^100+((i-sqrt3)/...

Prove that `((i+sqrt3)/2)^100+((i-sqrt3)/2)^100`+1=0.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

((-1+sqrt(3)i)/(2))^(100)+((-1-sqrt(3)i)/(2))^(100)=

Prove that (sqrt(3)/(2) +(i)/(2))^(5) + (sqrt(3)/(2) -(i)/(2))^(5) is purely real.

Prove that [(i+sqrt(3))/(-i+sqrt(3))]^(100)+[(i-sqrt(3))/(i+sqrt(3))]^(100)=-1

The value of (i+sqrt(3))^(100)+(i-sqrt(3))^(100)+2^(100) is

Prove that ((sqrt3+i)/(sqrt3-i)) ^(3n) +1=0 for all odd integral values of n.

Prove that ((i-sqrt(3))/(-i+sqrt(3)))^(200)+((i-sqrt(3))/(i+sqrt(3)))^(200)=-1

(sqrt3/2+i/2)^5 - (sqrt3/2-i/2)^5=

Write the comple number in a + ib form unsing cube roots of unity: (a) (-(1)/(2) + sqrt(3)/(2)i)^(1000) (b)If z =(sqrt(3) + i)^(17)/((1-i)^(50)) (c) (i + sqrt(3))^(100) + (i+ sqrt(3))^(100) + 2^(100)

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

    Text Solution

    |

  2. If x = a + b, y= aw + bw^2 and z = aw^2 + bw, where w is an imaginary ...

    Text Solution

    |

  3. Prove that ((i+sqrt3)/2)^100+((i-sqrt3)/2)^100+1=0.

    Text Solution

    |

  4. What is the value of ((i+sqrt3)/(-i+sqrt3))^(200)+((i-sqrt3)/(i+sqrt3)...

    Text Solution

    |

  5. Prove that sqrt(-1-sqrt(-1-sqrt1-… prop=w or w^2 .

    Text Solution

    |

  6. Resolve into the linear factor: a^3+b^3

    Text Solution

    |

  7. Resolve into the linear factor: a^3+b^3+c^3-3abc

    Text Solution

    |

  8. value of the series a(0)-a(2) + a(4)-a(6) +….. is

    Text Solution

    |

  9. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a1-a3+a5-a7+… .

    Text Solution

    |

  10. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a0+a3+a6+a9+… .

    Text Solution

    |

  11. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

    Text Solution

    |

  12. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : (1...

    Text Solution

    |

  13. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : 1+...

    Text Solution

    |

  14. If alpha is an n^(th) roots of unity, then 1+2alpha+3alpha^(2)+……..+n...

    Text Solution

    |

  15. If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + ...

    Text Solution

    |

  16. sum(p=1)^pi(3p+2)[sum(q=1)^10sin(2qpi)/11-icos(2qpi)/11]^p

    Text Solution

    |

  17. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

    Text Solution

    |

  18. If alpha ia ROOT OF x^2+x+1= 0 then show that alpha is also a root of...

    Text Solution

    |

  19. If p,q,r are three consecutive integers ge3, prove that x^p+x^q+x^r is...

    Text Solution

    |

  20. If n is n odd integer that is greater than or equal to 3 but not la ul...

    Text Solution

    |