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\begin{problem}(1.10)  \textit{Fix an } $a\in\mathbb{C}$ \textit{and } $b\in\mathbb{R}$ \textit{. Show $b\in\mathbb{R}$. \textit{Show  that the equation } $|z^{2}|+Re(az)+b=0$ \textit{has a solution if and only if }$|a^2|\geq4b$.  \end{problem}