Home
Class 12
MATHS
If w=cos""(pi)/(n)+isin""(pi)/(n) then v...

If `w=cos""(pi)/(n)+isin""(pi)/(n)` then value of `1+w+w^(2)+.......+w^(n-1)` is :

A

1 + i

B

`1 + itan (pi//2n)`

C

`1 + icot (pi//2n)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 13|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 14|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 11|1 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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_(0) + p_(4) + p_(8) + . . . = 2 ^(n//2-1) cos "" ( n pi)/( 4) + 2 ^(n-2)

+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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)]

Knowledge Check

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

    A
    `1 + i cot ((pi)/(2pi))`
    B
    `1 + i tan ((pi)/(n))`
    C
    1 + i
    D
    None of these

  • If n is an integer other than a multiple of 3, then the value of 1 + omega^(n) + omega^(2n) is

    A
    1
    B
    `-1`
    C
    0
    D
    3

    • Similar Questions

    Explore conceptually related problems

    + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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_(2) + p_(5) + p_(8) + . . . = (1)/( 3) [ 2^(n) + 2 cos ( n + 2) (pi)/(3)]

    + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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_(0) + p_(3) + p_(6) + . . . = (1)/(3) (2 ^(n) + 2 cos "" (n pi)/( 3))

    + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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 _(0) - p_(2) + p_(4) - . . . = 2^(n//2) cos ( n pi // 4)

    + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) + omega + omega^(2) = 0, omega = e^(2 pi 1//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_(3) + p_(5)- . . . = 2 ^(n//2) sin ( n pi // 4)

    Let alpha=(cos(2 pi))/(n)+i(sin(2 pi))/(n),n in N and let A_(k)=x+y alpha^(k)+z alpha^(2k)+...+w alpha^((n-1)k) where (k=0,1,2,...n-1) where x,y,z,...,u,w are n arbitrary complex numbers.Prove that sum_(k=0)^(n-1)|A_(k)|^(2)=n{|x|^(2)+|y|^(2)+|z|^(2)+...+|w|^(2)}

    Let omega_(n)=cos((2 pi)/(n))+i sin((2 pi)/(n)),i^(2)=-1 then (x+y omega_(3)+z omega_(3)^(2))(x+y omega_(3)^(2)+z omega_(3))=

    Home
    Profile