Let \(z,w\) be complex numbers satisyfing the following system:
\(
\begin{array}{r}
z - w = i \\
z + w = 2 \\
\end{array}
\)
What must be the value for the real part of \(z\)?
The answer is \(1\). Adding the two equations give \(2z = 2+i\).
So \(z = 1+\frac{1}{2}i\).