Level
2

Let \(m\) be a line in the complex plane defined by

\[(1-i)z+(1+i)\overline{z} =4.\]

Let \(z_1=2+2i\) be a point in the complex plane.

If the reflection of \(z_1\) in \(m\) is \(z_{2}\), then compute the value of

\[\overline{z_{1}}(1+i)+z_{2}(1-i).\]

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