Mathematics - Complex Number Question with Solution | TestHub

$$\begin{array}{rl}& |z|=\left|\left(z-\frac{4}{z}\right)+\frac{4}{z}\right|\Rightarrow |z|=\left|z-\frac{4}{z}+\frac{4}{z}\right|\\ & \Rightarrow |z|\le \left|z-\frac{4}{z}\right|+\frac{4}{|z|}\Rightarrow |z|\le 2+\frac{4}{|z|}\end{array}$$ $$\begin{array}{rl}& \Rightarrow |z{|}^2-2|z|-4\le 0\\ & (|z|-(\sqrt{5}+1))(|z|-(1-\sqrt{5}))\le 0\Rightarrow 1-\sqrt{5}\le |z|\le \sqrt{5}+1\end{array}$$