# Determining a Möbius transformation image [closed]

so I was attempting a question on Möbius transformations and I've encountered a problem in my workings. The question is "Determine the image of the strip $$-1 < \Re(z) < 1$$ under $$g(z) = (iz+1)/(z+1).$$ How should I go about solving this?

So if you know the images of three points on one boundary line of the strip (say $$1$$ and $$1\pm i$$), then you know the circle-or-line that is the image of that boundary line; similarly, if you know you know the images of three points on the other boundary line (say $$-1$$ and $$-1\pm i$$), then you know the circle-or-line that is the image of this other boundary line; and if you know the image of a point inside the strip (say $$0$$), then you know which side of the image circles-or-lines is the interior of the image region.