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Question

If z is a nonreal root of 71, then the value of z86+z175+z289

A
i
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B
i
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C
1
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D
1
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Solution

The correct option is C 1
Let z=71. Then
z7=1
z86+z175+z289
=(z7)12×z2+(z7)25+(z7)41×z2
=(1)12×z2+(1)25+(1)41×z2
=z21z2=1

Hence, option C.

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