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# Question

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let $$z_1,z_2$$and $$z_3$$ be complex numbers such that: \begin{align} \overline{z_1}&=\dfrac{1}{z_1}\\ \overline{z_2}&=\dfrac{2}{z_2}\\ z_3&=z_1+z_2. \end{align}. What is the product of the minimum and maximum possible values of $$|z_3|?$$

Oct 22, 2022