TITLE: Interpret to a complex plane!
QUESTION [10 upvotes]: $\newcommand{\Re}{\operatorname{Re}}\newcommand{\Im}{\operatorname{Im}}$The question is: 
Interpret
$$
\Re z + \Im z = 1
$$
geometrically in the complex plane. 
Writing $z = x + yi$, the condition $\Re z + \Im z = 1$ becomes
$x + y = 1$.
Now should we rearrange $y = 1 - x$ and say it is a line that crosses the two coordinates $(0, 1)$ and $(1, 0)$? Or am I way off on this one? :/

REPLY [6 votes]: You are spot-on. This is simply the line in the plane $x + y = 1$.