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Question

1,z1,z2,z3,,zn1 are the nth roots of unity, then the value of 13z1+13z2++13zn1 is equal to

A
n.3n13n1+12
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B
n.3n13n11
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C
n.3n13n1+1
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D
n.3n13n112
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Solution

The correct option is D n.3n13n112
zn1=(z1)(zz1)(zz2)(zzn1)
Differentiating w.r.t. X
nzn1zn1=1z1+1zz1++1zzn1

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