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If alpha is a complex number such that a...

If `alpha` is a complex number such that `alpha^(2)+alpha+1=0`, then the value of `alpha^(61)` is

A

1

B

`-1`

C

`alpha`

D

`-alpha`

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Knowledge Check

  • If A=[(alpha,2),(2,alpha)] and |A^(3)|=125 , then the value of alpha is -

    A
    `pm2`
    B
    `pm3`
    C
    `pm5`
    D
    0

  • For a real number alpha , let A(alpha) denote the matrix ((cosalpha,sinalpha),(-sinalpha,cosalpha)) . Then for real numbers alpha_(1) and alpha_(2) , the value of A(alpha_(1))A(alpha_(2)) is -

    A
    `A(alpha_(1)alpha_(2))`
    B
    `A(alpha_(1)+alpha_(2))`
    C
    `A(alpha_(1)-alpha_(2))`
    D
    `A(alpha_(2)-alpha_(1))`

  • If cos 9alpha = sin alpha and 9 alpha lt 90^@ , then the value of tan 5 alpha is

    A
    `1/sqrt3`
    B
    `sqrt3`
    C
    1
    D
    0

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