Complex Geometry

Algebra Level 4

If $$a\bar{z}+\bar{a}z+1=0$$ and $$b\bar{z}+\bar{b}z-1=0$$ are two mutually perpendicular lines where $$a$$ and $$b$$ are two non-zero fixed complex numbers, $$z$$ is a variable complex number then which of these holds ?

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