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Question

If α(1) is a fifth root of unity then log31+α+α2+α323=

A
1
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B
2
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C
3
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D
12
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Solution

The correct option is B 2
If z51=0
(z1)(z4+z3+z2+z+1)=0
z4+z3+z2+z+1=0
z3+z2+z+1+1z=0
α3+α2+α+1=1α
1+α+α2+α32α=1α2α
1+α+α2+α32α=3α$
α=1,i,i
α=1ii=1
log31+α+α2+α32α=log33
=log3(32)
=2


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