Do they represent conic sections?

Algebra Level 4

{z+zˉ+zzˉ=2iz1+zi=2\begin{cases} |z+\bar{z}|+|z-\bar{z}|=2 \\ |iz-1|+|z-i|=2\end{cases} Find the complex number zz which does not satisfy the above equations simultaneously.

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