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(sqrt3+i)^(12)=...

`(sqrt3+i)^(12)`=

A

`2^6`

B

`2^8`

C

`2^9`

D

`2^(12)`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

    A
    1
    B
    `sqrt3`
    C
    `sqrt2`
    D
    2

  • Imaginary part of (sqrt3-i)^(2016)+(-sqrt3-i)^(2019) is

    A
    `2^(2016)`
    B
    `-2^(2016)`
    C
    `-2^(2019)`
    D
    `2^(2019)`

  • The values of (sqrt3+i)^(1//4) are

    A
    `2^(1//4)cis[(2kpi+pi//6)/(4)],k=0,1,2,3`
    B
    `2^(1//4)cis[(2kpi+pi//3)/(4)],k=0,1,2,3`
    C
    `2^(1//4)cis[(2kpi-pi//6)/(4)],k=0,1,2,3`
    D
    `2^(1//4)cis[(2kpi-pi//3)/(4)],k=0,1,2,3`

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