Home
Class 12
MATHS
I : sum(k=1)^(6)[sin((2kpi)/(7))-icos((2...

`I : sum_(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=i`
`II : sum_(r=1)^(8)[sin((2pir)/(9))+icos((2pir)/(9))]=i`
Which of the above statements are true

A

A) only I

B

B) only II

C

C) Both I and II

D

D) neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE -II|58 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

sum_(r =1)^(16) ( sin [(2r pi)/(17)] + icos [(2rpi)/(17)] ) =

Find the value of sum_(k=1)^(10){sin((2kpi)/(11))-i cos ((2kpi)/(11))}

The value of prod_(k=1)^6((sin)(2pik)/(7)-(icos)(2pik)/(7)) is

The values of sum_(m=1)^(10)[sin(2pim//11)-icos(2pim//11)] is

If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=

I : Value of i^i=e^(-pi/2) II : z=ilog(2+sqrt3) then sinz=2 which of above statement is true

Consider the following statements. I. sin^(-1)(y^2-4y+6)+ cos^(-1)(y^2-4y +6)= pi/2, AA y in R II. sec^(-1)(y^2-4y+6)+ cosec^(-1)(y^2-4y+6)= pi/2, AA y in R Which of the above statements (s) is / are true ?

AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

    Text Solution

    |

  2. If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, the...

    Text Solution

    |

  3. A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^...

    Text Solution

    |

  4. Assertion (A): If A, B, C are the angles of a triangle such that cos A...

    Text Solution

    |

  5. IF omega represents a complex cube root of unity, then (1+1/omega)(1+1...

    Text Solution

    |

  6. Assertion (A) : If alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^...

    Text Solution

    |

  7. If z=(sqrt3-i)/(2) then (i^(101)+z^(101))^(103)=

    Text Solution

    |

  8. The roots of (z-1)^n=i(z+1)^n are plotted on the argand plane they are

    Text Solution

    |

  9. If 'alpha' be the non-real n^(th) roots of unity, then 1+3alpha+5alpha...

    Text Solution

    |

  10. If cos alpha+2cos beta+3cos gamma=sinalpha+2sinbeta+3singamma=0 then s...

    Text Solution

    |

  11. If sin(A+iB)=x+iy then ((x^2)/(sin^2A)-(y^2)/(cos^2A))+((x^2)/(cosh^2B...

    Text Solution

    |

  12. I : sum(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=i II : sum(r=1)...

    Text Solution

    |

  13. Match the following. {:(Column-I," "Column-II),(I" : "x=costheta...

    Text Solution

    |

  14. The ascending order of the values of z1(1+i)^4+(1-i)^4, z2=(sq...

    Text Solution

    |

  15. I : Value of i^i=e^(-pi/2) II : z=ilog(2+sqrt3) then sinz=2 wh...

    Text Solution

    |

  16. Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2c...

    Text Solution

    |

  17. The modulus argument form of 1+iTantheta when theta epsilon (pi/2,pi) ...

    Text Solution

    |

  18. If Z=(i^i)^i" where "i=sqrt(-1) then

    Text Solution

    |

  19. If alpha is a non-real and alpha=(1)^(1//5) then the value of 2^(|1+al...

    Text Solution

    |

  20. If (x-1)^4-16=0,then the sum of non-real complex values of x is

    Text Solution

    |