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The rea part of (1-i)^(-i),"where" i=sqr...

The rea part of `(1-i)^(-i),"where" i=sqrt(-1)`is

A

`e^(-pi//4)cos((1)/(2)log_(e)2)`

B

`-e^(-pi//4)sin((1)/(2)log_(e)2)`

C

`e^(-pi//4)cos((1)/(2)log_(e)2)`

D

`e^(-pi//4)sin((1)/(2)log_(e)2)`

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The real part of (1-i)^(-i) is

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Knowledge Check

  • What is the principal argument of (-1-i), where i=sqrt(-1) ?

    A
    `(pi)/(4)`
    B
    `-(pi)/(4)`
    C
    `-(3pi)/(4)`
    D
    `(3pi)/(4)`

  • What is the principle argument of ( -1-i) where i = sqrt( - 1) .

    A
    A) `(pi)/( 4)`
    B
    B) `- ( pi )/( 4)`
    C
    C) `- ( 3pi )/( 4)`
    D
    D) `( 3pi )/( 4)`

  • What is the square root of i, where i=sqrt(-1) ?

    A
    `(1+i)/(2)`
    B
    `(1-i)/(2)`
    C
    `(1+i)/(sqrt2)`
    D
    None of these

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    Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purly imaginary with positive imaginary part.

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