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Let $c$ is complex-number satisfying :

$(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$

So, how could i get $(3c^{100}+\frac{2}{c^{100}}+1)(c^{100}+\frac{2}{c^{100}}+3)$ ?

freeze
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    Please formulate it as a question rather than a statement. Though most people probably understand what you are asking, it may not be obvious to some non-native speakers. – Mårten W Apr 17 '13 at 08:02

1 Answers1

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HINT:

On simplification, $c^4+c^3+c^2+c+1=0$

Clearly, $c\ne1$

Multiply either sides the $(c-1),$ we get $c^5-1=(c-1)\cdot0=0$

$\implies c^5=1\implies c^{100}=(c^5)^{20}=1$

lab bhattacharjee
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