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Question

Let z is a complex number satisfying the equation Z6+Z3+1=0. If this equation has a root reiθ with 90o<θ<180o then the value of theta is

A
100o
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B
110o
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C
160o
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D
170o
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Solution

The correct option is C 160o
Let y=z3

Then Get y2+y+1=0

it is cube Root of unity

Represented as :

w=e2ni3 & w2=e4ni3,

y=e2kni3,k0,

Take z=e2kπi9

z=e2πi9,e4π9,e8π9,e10π9e14π9,e16π9

for 90<θ<180

θ=8×1809=160

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