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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