Question

If w is a complex cube root of unity then find the value of
$w + \frac{1}{w}$
​

Answer 1

Step-by-step explanation:

$w \: + \: \frac{ 1}{w} \\ \\ \: multiply \: \frac{1}{w} \: on \: both \: sides \\ \: with \: {w}^{2} . \\ \\ we \: get \: = > \\ \frac{ {w}^{2} }{ {w}^{3} } \\ \\ we \: know \: that \: {w}^{3} = 1 \\ \\ = > \frac{ {w}^{2} }{1} = {w}^{2} \\ \\ w + {w}^{2} \\ = - 1 \\ \\ (as \: 1 + w + {w}^{2} = 0)$

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