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1. The problem statement, all variables and given/known data

Find the greatest value of the moduli of the complex numbers [itex]z[/itex] satisfying the equation

[itex]|[/itex][itex]z[/itex] - [itex]\frac{4}{z}[/itex][itex]|[/itex] = 2

3. The attempt at a solution

I tried letting [itex]z[/itex] = [itex]a+bi[/itex] and going from there, but I ended up with this really large equation:

[itex]\left(\frac{a\left(a^{2} + b^{2} - 4\right)}{a^{2} + b^{2}}\right)^{2} + \left(\frac{b\left(a^{2} + b^{2} + 4\right)}{a^{2} + b^{2}}\right)^{2}[/itex] = 4

and I don't know how to simplify it. And even if I did simplify it, I don't know how I would find the greatest value of the moduli of [itex]z[/itex].

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# Greatest Moduli Complex Number Solution of Equation

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