(a) Count the number of roots of ω of the equation z2019−1=0 over complex numbers that satisfy
\begin{align*}
\vert \omega + 1 \vert \geq \sqrt{2 + \sqrt{2}}
\end{align*}
(b) Find all real numbers x that satisfy following equation :
\begin{align*}
\frac{ 8^x + 27^x }{ 12^x + 18^x } = \frac{7}{6}
\end{align*} complex numbersDiophantine equationCMIalgebra