Complex Equations

Algebra Level 4

(23i)z+(5+i)w=194i(1i)z+(2+i)w=9i\begin{aligned} (2-3i)z + (5+i)w &= 19-4i\\ (1-i)z + (2+i)w &= 9-i \end{aligned}

Let zz and ww be the complex numbers satisfying the equations above.

Compute z+w2|z+w|^2.

Note: i2=1i^2 = -1, and z|z| is the absolute value of zz.

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