First slide

Algebra of complex numbers

Question

$If |z - \frac{4}{z}| = 2 then the maximum value of | z | is equal to$

Moderate

Solution

$\begin{array}{l} | z | = |(z - \frac{4}{z}) + \frac{4}{z}| \leq |z - \frac{4}{z}| + \frac{4}{| z |} \\ | z | \leq 2 + \frac{4}{| z |} \\ | z |^{2} - 2 | z | - 4 \leq 0 \\ 1 - \sqrt{5} \leq | z | \leq \sqrt{5} + 1 \end{array}$

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