Make the complex simple

Level 2

Let mm be a line in the complex plane defined by

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

Let z1=2+2iz_1=2+2i be a point in the complex plane.

If the reflection of z1z_1 in mm is z2z_{2}, then compute the value of

z1(1+i)+z2(1i).\overline{z_{1}}(1+i)+z_{2}(1-i).

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