\begin{equation*} \ ||z_{1}|-|z_{2}||\le|z_{1}+z_{2}|\le|z_{1}|+|z_{2}| \end{equation*} The second inequality follows from the triangle...
\(z^{n}+\overline{z}^{n}\) is a real number for all positive \(n\). Proof 1 Treat \(z=re^{i\theta}\) and you can show that the sum...