Discussion
The equation \(\mathrm{Im}(1 - i)z = 1\) represents the line
Answer: A
The equation represents the line \(y = x + 1\).
Write \(z = x + iy\) and multiply out.
\[ \begin{aligned} (1 - i)(x + iy) &= x + iy - ix - i^{2}y \\ &= (x + y) + i(y - x) \end{aligned} \]
The imaginary part is \(y - x\), so \(y - x = 1\), that is \(y = x + 1\). Taking the real part by mistake gives \(x + y = 1\), the option \(y = 1 - x\), and a sign slip in \(-i^{2}y\) produces the other lines.
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