# Showing a specific (complex) point in a Graphic [closed]

Somewhat related to a previous post that I made - Complex infinity at a point and division by zero

I'm still following the book on this example and I've come to the part where one draws the 'paradoxical' sets on the Poincaré disk, the code of which is:

PoincareImage1 =
Graphics[{EdgeForm[Thickness[0.005]], {col1, Disk[]}, {col3,
blueLeft}, {col2, greenMiddle}, {col1,
Polygon[project1 /@ ToC[redTail]]}, {col3,
Polygon[project1 /@ ToC[blueTail]]}, {col2,
Polygon[project1[greenTop]],
Polygon[project1 /@ ToC[greenTail]]}}]


which produces the left image shown below. However, I want to explicitly plot/show the point i as is shown on the right image below.

I've tried adding it via the PointSize and Point specifications but to no avail. If necessary, I can post snippets of code that define the functions used in the portion I copied above but I don't believe it matters much in this scenario.

• This is a very poorly posed question. It neglects to mention the the most critical information needed: the sequence of graphics primitives that define the graphic for the point i. That said, I would add that for such primitives to produce a visible point, it must appear at the end of the iist of graphic primitives given to Graphics – m_goldberg Jun 5 '19 at 3:20
• By graphics primitives that define the graphic for $i$, do you mean the following: {x_?NumericQ, y_} :> f[x + I y], {PointSize[0.02], GrayLevel[1], Point[f[I]]}, Text[Style[I, 14], f[I] + {-0.06, 0.06}]}? Because if so, I've mentioned below the picture that doing this yields no result, or rather, pops up an error stating "An improperly formatted option was encountered. The left-hand side of the option was not a symbol or string." If that's not what you meant, I sincerely apologize, but I'd then need clarification of what the graphics primitives for $i$ are. – Kandrax Jun 5 '19 at 9:47

Your comment gives some clarification. It is clear from it that you specified the graphic primitives for drawing your point and its label in a way that makes no sense to Mathematica. I also infer that you want to specified the point's location as complex number. That is a weak inference, but I will go with it.

Since you still give no actual method for computing where the point is located, I will assume for purposes of providing an exammpe that the location is given by

z = .25 (Cos[45 °] + I Sin[45 °])


0.176777 + 0.176777 I

The following should show you how to specify your point in a Graphics expression.

Module[{i = ReIm[z]},
Graphics[
{EdgeForm[Thickness[0.005]],
{White, Disk[]},
{PointSize[0.02], Point[i], Text[Style["i", 14], i + {-0.06, 0.06}]}}]]


### Notes

1. You can not use I as a variable. It is reserved in Mathematica for the constant Complex[0,1]; i.e., Sqrt[-1].
2. I am not sure what you mean by the very strange expression

{x_?NumericQ, y_} :> f[x + I y]


but I am guessing you are trying to reinvent the built-in function ReIm. which I use in my example.

3. GrayLevel[1] is the same as White, so I used White`