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Question

The value of 10k=1(sin2kπ11+icos2kπ11) is

A
1
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B
10i
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C
i
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D
10i
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Solution

The correct option is A i
s=10k=1sin2kπ11+icos2kπ11=>s=10k=1ie2kπ11i=>s=i10k=1(e2iπ11)k=>s=i(e2iπ11+e4iπ11+....+e20iπ11)=>s=i(e2iπ11((e2iπ11)101)(e2iπ11)1)=>s=i(e22iπ11e2iπ11e2iπ111)=>s=i(e2iπe2iπ11e2iπ111)=>s=i(e2iπ=1)

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