If I understand the question correctly, you have a triangle in the complex plane, with vertices at 0, 2 and 2i, and you want to find its image under the map .

The image of the side [0,2] is the segment on the real axis. The image of the side [0,2i] is the segment on the imaginary axis.

The remaining side is a segment of the line , where . Let and write . Then . Take real and imaginary parts to see that and . Then the equation becomes . Rewrite this as . This represents a circle centred at , with radius .

The image of the third side of the triangle is therefore part of that circle, namely the part lying in the fourth quadrant. The image of the triangle and its interior is the whole of the fourth quadrant apart from the interior of that circle.