A widget that lets you pick a complex number:

TODO

• put in package
• drop shadow?
• smaller?
• show the currently picked point? or that should be in PlutoImageCoordinatePicker.jl ?

### A Pluto.jl notebook ###
# v0.19.43

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ f0c0a310-4069-11ef-316e-57f168e56249
using PlutoUI

# ╔═╡ 4130f271-a813-4064-b1b6-c86134fcf65e
using PlutoImageCoordinatePicker

# ╔═╡ da9a6e66-184f-4332-a175-963e6534c97d
md"""
# Usage

Click somewhere to pick a point!
"""

# ╔═╡ d48df3bf-624d-47dd-a3bc-ac32503946fd
md"""
# Implementation
"""

# ╔═╡ 57617007-3695-4e86-b8db-7be3737abd84
begin
	struct SVG
		content
	end

	function Base.show(io::IO, m::MIME"image/svg+xml", s::SVG)
		write(io, s.content)
	end
end

# ╔═╡ 55e7af24-5be1-4fb4-90b0-151478c2117a
im_axes = """<svg xmlns="http://www.w3.org/2000/svg" width="300" height="300" viewBox="0 0 300 300" style="max-width:100%;height:auto;color:black">

<defs>
    <marker id="triangle" viewBox="0 0 10 10" refX="1" refY="5" markerUnits="strokeWidth" markerWidth="10" markerHeight="10" orient="auto-start-reverse">
      <path d="M 0 0 L 10 5 L 0 10 z" fill="currentColor"></path>
    </marker>
  </defs>

<rect width="300" height="300" fill="white" rx="1em"/>

<line x1="10" x2="290" y1="150" y2="150" stroke="currentColor" marker-start="url(#triangle)" marker-end="url(#triangle)"></line>

<line y1="10" y2="290" x1="150" x2="150" stroke="currentColor" marker-start="url(#triangle)" marker-end="url(#triangle)"></line>
<circle cx="150" cy="150" r="3" fill="currentColor"></circle>

<g style="    font-family: math;
    font-style: italic;
    font-size: 17px;">

<g transform="translate(260, 140)">
<text fill="currentColor">Real</text>
</g>

<g transform="translate(170, 50) rotate(-90)">
<text text-anchor="middle" fill="currentColor">Imaginary</text>
</g>


<g transform="translate(150, 150)">
<text text-anchor="end" fill="currentColor" dx="-10" dy="20">0</text>
</g>



<g transform="translate(270, 150)">
<line y1="-5" y2="5" stroke="currentColor"></line>
<text text-anchor="middle" fill="currentColor" dy="20">1</text>
</g>
<g transform="translate(30, 150)">
<line y1="-5" y2="5" stroke="currentColor"></line>
<text text-anchor="middle" fill="currentColor" dy="20">-1</text>
</g>





<g transform="translate(150, 30)">
<line x1="-5" x2="5" stroke="currentColor"></line>
<text text-anchor="end" fill="currentColor" dy=".5ch" dx="-10">i</text>
</g>
<g transform="translate(150, 270)">
<line x1="-5" x2="5" stroke="currentColor"></line>
<text text-anchor="end" fill="currentColor" dy=".5ch" dx="-10">-i</text>
</g>



</g>

</svg>""" |> SVG

# ╔═╡ 1a1addef-b075-4b17-aa2f-c70f4f86d421
function ComplexNumberPicker()
	PlutoUI.Experimental.transformed_value(ImageCoordinatePicker(im_axes)) do point
		if point === nothing
			nothing
		else
			t(x) = (x - 150.0) / 120.0
			t(point.x) - im * t(point.y)
		end
	end
end

# ╔═╡ 2e4d8a7a-a798-4bec-a724-03ad82ae2c22
@bind point ComplexNumberPicker()

# ╔═╡ 618f145d-4d5f-4357-ba71-3169bd797f59
point

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
PlutoImageCoordinatePicker = "79686372-6169-7274-6170-6568746b6366"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
PlutoImageCoordinatePicker = "~1.2.0"
PlutoUI = "~0.7.59"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.10.3"
manifest_format = "2.0"
project_hash = "d49b41fcbd086d01c85d7eed4eab20544187de0b"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.2"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.5"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.5"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.5"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.5"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "b6d6bfdd7ce25b0f9b2f6b3dd56b2673a66c8770"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.5"

[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.4"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.4.0+0"

[[deps.LibGit2]]
deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.6.4+0"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.0+1"

[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[deps.LinearAlgebra]]
deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"

[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.2+1"

[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2023.1.10"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.23+4"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.1"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.10.0"

[[deps.PlutoImageCoordinatePicker]]
deps = ["AbstractPlutoDingetjes", "HypertextLiteral", "InteractiveUtils", "Markdown"]
git-tree-sha1 = "7c977ad2c6461553d80840e507911e10de17a503"
uuid = "79686372-6169-7274-6170-6568746b6366"
version = "1.2.0"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "ab55ee1510ad2af0ff674dbcced5e94921f867a9"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.59"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.3"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.10.0"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.10.0"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.2.1+1"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.Tricks]]
git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.8"

[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"
"""

# ╔═╡ Cell order:
# ╟─da9a6e66-184f-4332-a175-963e6534c97d
# ╠═2e4d8a7a-a798-4bec-a724-03ad82ae2c22
# ╠═618f145d-4d5f-4357-ba71-3169bd797f59
# ╟─d48df3bf-624d-47dd-a3bc-ac32503946fd
# ╠═f0c0a310-4069-11ef-316e-57f168e56249
# ╠═4130f271-a813-4064-b1b6-c86134fcf65e
# ╠═1a1addef-b075-4b17-aa2f-c70f4f86d421
# ╠═57617007-3695-4e86-b8db-7be3737abd84
# ╟─55e7af24-5be1-4fb4-90b0-151478c2117a
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002