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and  $$Re(az)=fd-eg$$  So $$|z^{2}|+Re(az)+b=0 $$|z^{2}|+Re(az)+b=0$$  \text{has solutions}$$ solutions}  \begin{align}  \iff (f^{2}+g^{2})+(fd-eg)+b=0\\  \iff f^{2}+fd+g^{2}-eg+b=0\\