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Suppose I have to sketch the set $\{z=a+bi \mid a+b<2\}$. Is there an ideal or principled way of approaching this? My approach was to simply consider $b<-a+2$ or $a<-b+2$ which may be viewed as either shifting the solution set to the right two units (real part with two added) or shifting the entire solution set up two units (imaginary part with two added).

Is there a better / more natural way of looking at this?

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    The boundary is a line. Find two points on the line, such as $2$ and $2i$, then draw the line between those points. Your region is on one side of the bounding line. – 2017-01-22

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In is simply the half-plane under the straight line with equation $\;a+b=2$, which is the line through $(2,0)$ and $(0,2)$ in the complex plane identified with $\mathbf R^2$.