Question: $\omega$ is an imaginary cube root of unity. If $(1 + \omega^{2})^{m} = (1 + \omega^{4})^{m},$ t...

Question

$\omega$ is an imaginary cube root of unity. If $(1 + \omega^{2})^{m} = (1 + \omega^{4})^{m},$ then least positive integral value of m is

Answer 1

Sol. The given equation reduces to $( - \omega)^{m} = ( - \omega^{2})^{m}$

⇒ $\omega^{m} = 1$

⇒ $m = 3$ .

Question: \(\omega\) is an imaginary cube root of unity. If \((1 + \omega^{2})^{m} = (1 + \omega^{4})^{m},\) t...