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Simplify: [(1+sin pi/8+i cos pi/8)/(1+si...

Simplify: `[(1+sin pi/8+i cos pi/8)/(1+sin pi/8-i cos pi/8)]^(1/2)`

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[(1+sin(pi//8)+icos(pi//8))/(1+sin(pi//8)-icospi//8)]^(-8//3)

Show that one value of ((1 + sin . pi/8 + i cos . pi/8)/(1 + sin . pi/8 - i cos . pi/8))^(8//3) " is " - 1 .

Knowledge Check

  • ((sin (pi/8)+i cos (pi/8))/(sin (pi/8)-i cos (pi/8)))^(8)=

    A
    a.-1
    B
    b.0
    C
    c.1
    D
    d.2i

  • The smallest positive integral value of ' n ' such that [(1+sin (pi)/(8)+i cos (pi)/(8))(1+sin (pi)/(8)-i cos (pi)/(8))]^(n) is purely imaginary is

    A
    2
    B
    8
    C
    4
    D
    3

  • The smallest positive integral value of n such that [(1+"sin"pi/8+i"cos"(pi)/8)/(1+"sin"(pi)/8-i"cos"(pi)/8)]^(n) is purely imaginary is n=

    A
    2
    B
    8
    C
    4
    D
    3

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    Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i cos"" pi/8))^(8/3)=-1

    " **4.Show that one value of "((1+sin(pi)/(8)+i cos(pi)/(8))/(1+sin(pi)/(8)-i cos(pi)/(8)))^((8)/(3))=-1

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    The expression [(1+sin((pi)/(8))+i cos((pi)/(8)))/(1+sin((pi)/(8))-i cos((pi)/(8)))]^(8)

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