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