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Question

⎜ ⎜1+cosπ8isinπ81+cosπ8+isinπ8⎟ ⎟8=

A
1
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B
1
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C
2
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D
12
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Solution

The correct option is B 1
We know that cosθ+isinθ=eiθ
⎜ ⎜ ⎜ ⎜1+cos(π8)isin(π8)1+cos(π8)+isin(π8)⎟ ⎟ ⎟ ⎟8=⎜ ⎜ ⎜1+eiπ81+eiπ8⎟ ⎟ ⎟8=⎜ ⎜1eiπ8⎟ ⎟8=eiπ=1
Therefore correct option is B

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