# Make the complex simple

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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