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Show that one value of ((1 + sin . pi/...

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`.

Answer

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Knowledge Check

  • cos. (pi)/(13) + cos. (5pi)/(13) + cos. (8pi)/(13) + cos. (12pi)/(13)=

    A
    0
    B
    1
    C
    -1
    D
    2

  • The amplitude of sin pi/5 +I (1- "cos" pi/5) is

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    B
    `pi/10`
    C
    `pi/5`
    D
    `(2pi)/(5)`

  • The value of cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15) is

    A
    `1/16`
    B
    `1/8`
    C
    `1/12`
    D
    `1/4`

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    ((1 + "cos"(pi)/(8) -i "sin"(pi)/(8))/(1 + "cos"(pi)/(8) + i "sin" (pi)/(8)))^(12)=

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