# Complex Optimization

Algebra Level 5

Maximize $$\alpha$$ if there is exists a complex number $$z$$ satisfying \begin{align} &|z| =3\\ &|z-(\alpha-1)i-\alpha| \leq 3 \\ &|z-(\alpha+1)i+2\alpha| >3 \end{align}

Details and Assumptions

• $$\alpha$$ can only be real.
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