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Question: How do I plot complex transformations?

Question:How do I plot complex transformations?

jgray07m 15 Maple 2019
complex transformation plotting
December 06 2019
2

I have a region that can be graphed by A := plots:-inequal([evalc(abs(z)) < 3, evalc(1 < abs(z - 1))], x = -5 .. 5, y = -5 .. 5)

From there, I need to use the transformation 

M := (3 + sqrt(5))/2*(z - x1)/(z - x2) where x1 := (9 - sqrt(45))/2 and x2 := (9 + sqrt(45))/2 

 

How do I do this? Do I need to extract data points from the first graph? Is there an easier way to do this? 
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