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Question

The continued product of the four values of [cos(π3)+isin(π3)]3/4 is

A
1
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B
1
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C
2
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D
2
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Solution

The correct option is B 1
We have, [cos(π3)+isin(π3)]3/4
=(cosπ+isinπ)1/4
Let z=(cosπ+isinπ)1/4
z4=cosπ+isinπ=1
If z1,z2,z3,z4 are the roots then
z1z2z3z4=1(1)41=1

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