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$\newcommand{\Re}{\operatorname{Re}}\newcommand{\Im}{\operatorname{Im}}$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? :/

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You showed your effort so far: this is a great habit for posting on this forum. – ncmathsadist Aug 18 '14 at 11:55
Thank you @ncmathsadist, Am all about the learning and understand the principals :) – Ara Aug 18 '14 at 12:16
up vote 6 down vote accepted

You are spot-on. This is simply the line in the plane $x + y = 1$.

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Awesome, thank you :) – Ara Aug 18 '14 at 12:16

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