Let \( \bar{b} z+b \bar{z}=c, b \neq 0 \), be a line in the complex plane, where \( \bar{b} \) i...

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Let \( \bar{b} z+b \bar{z}=c, b \neq 0 \), be a line in the complex plane, where \( \bar{b} \) is the complex conjugate of \( b \). If a point \( z_{1} \) is the
P reflection of the point \( z_{2} \) through the line, then show

W that \( c=\bar{z}_{1} b+z_{2} \bar{b} \).
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