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Fix a ∈ C and b ∈ R. Show that the equation |z2|+Re(az)+b = 0 has...

Fix a ∈ C and b ∈ R. Show that the equation |z2|+Re(az)+b = 0 has a solution if and only if |a2| ≥ 4b. When solutions exist show the solution set is a circle. (proof in the form of a generic If and only if proof).

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