An Argand diagram plots complex numbers as points in the complex plane, with the real part on the x-axis and the imaginary part on the y-axis. Vectors from the origin to each point illustrate magnitude and phase angle, while a unit circle provides a geometric reference. This visualization is foundational for complex analysis, signal processing, and understanding operations like addition, multiplication, and roots of unity geometrically.
# anyplot.ai
# scatter-complex-plane: Complex Plane Visualization (Argand Diagram)
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 88/100 | Created: 2026-06-02
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const IMPRINT_PALETTE = [
colorant"#009E73", # 1 — brand green (first series)
colorant"#C475FD", # 2 — lavender
colorant"#4467A3", # 3 — blue
colorant"#BD8233", # 4 — ochre
colorant"#AE3030", # 5 — matte red
colorant"#2ABCCD", # 6 — cyan
colorant"#954477", # 7 — rose
colorant"#99B314", # 8 — lime
]
# Data — 5th roots of unity: e^(2πik/5) for k = 0,...,4
n_roots = 5
theta_roots = [2π * k / n_roots for k in 0:(n_roots - 1)]
re_roots = cos.(theta_roots)
im_roots = sin.(theta_roots)
root_labels = ["z₀", "z₁", "z₂", "z₃", "z₄"]
# Arbitrary complex numbers outside the unit circle
re_arb = [1.5, -1.3, 0.6]
im_arb = [1.1, 0.8, -1.7]
arb_labels = ["w₁", "w₂", "w₃"]
# Unit circle reference (parametric)
theta_circle = LinRange(0, 2π, 300)
# Figure — square canvas: size=(1200,1200) × px_per_unit=2 → 2400×2400 px
fig = Figure(
size = (1200, 1200),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "scatter-complex-plane · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Re(z)",
ylabel = "Im(z)",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = (INK_SOFT, 0.12),
ygridcolor = (INK_SOFT, 0.12),
aspect = DataAspect(),
)
# Unit circle — dashed reference
lines!(ax, cos.(theta_circle), sin.(theta_circle);
linestyle = :dash,
color = (INK_SOFT, 0.8),
linewidth = 1.5,
)
# Real and imaginary axis lines through origin
hlines!(ax, [0.0]; color = (INK_SOFT, 0.5), linewidth = 0.8)
vlines!(ax, [0.0]; color = (INK_SOFT, 0.5), linewidth = 0.8)
# Arrows from origin to 5th roots of unity
roots_origins = fill(Point2f(0, 0), n_roots)
roots_dirs = Point2f.(re_roots, im_roots)
arrows!(ax, roots_origins, roots_dirs;
color = IMPRINT_PALETTE[1],
linewidth = 2.0,
arrowsize = 16,
)
# Arrows from origin to arbitrary complex numbers
arb_origins = fill(Point2f(0, 0), length(re_arb))
arb_dirs = Point2f.(re_arb, im_arb)
arrows!(ax, arb_origins, arb_dirs;
color = IMPRINT_PALETTE[2],
linewidth = 2.0,
arrowsize = 16,
)
# Scatter points — 5th roots of unity (circle markers)
scatter!(ax, re_roots, im_roots;
color = IMPRINT_PALETTE[1],
markersize = 14,
marker = :circle,
strokewidth = 1.5,
strokecolor = PAGE_BG,
label = "5th roots of unity",
)
# Scatter points — arbitrary complex numbers (diamond markers for shape encoding)
scatter!(ax, re_arb, im_arb;
color = IMPRINT_PALETTE[2],
markersize = 14,
marker = :diamond,
strokewidth = 1.5,
strokecolor = PAGE_BG,
label = "Arbitrary complex",
)
# Labels for roots of unity — symbolic name + rectangular form annotation
label_offset = 0.18
for (r_val, i_val, lbl) in zip(re_roots, im_roots, root_labels)
mag = sqrt(r_val^2 + i_val^2)
ox = r_val / mag * label_offset
oy = i_val / mag * label_offset
h = r_val > 0.1 ? :left : (r_val < -0.1 ? :right : :center)
v = i_val > 0.1 ? :bottom : (i_val < -0.1 ? :top : :center)
# Symbolic label
text!(ax, [Point2f(r_val + ox, i_val + oy)];
text = [lbl],
fontsize = 14,
color = INK,
align = [(h, v)],
)
# Rectangular form — placed further out along the same radial direction
rect_str = i_val >= 0 ?
"$(round(r_val, digits=2))+$(round(i_val, digits=2))i" :
"$(round(r_val, digits=2))$(round(i_val, digits=2))i"
rox = r_val / mag * (label_offset + 0.24)
roy = i_val / mag * (label_offset + 0.24)
text!(ax, [Point2f(r_val + rox, i_val + roy)];
text = [rect_str],
fontsize = 10,
color = INK_SOFT,
align = [(h, v)],
)
end
# Labels for arbitrary complex numbers — symbolic name + rectangular form annotation
for (r_val, i_val, lbl) in zip(re_arb, im_arb, arb_labels)
mag = sqrt(r_val^2 + i_val^2)
ox = r_val / mag * 0.2
oy = i_val / mag * 0.2
h = r_val > 0 ? :left : :right
v = i_val > 0 ? :bottom : :top
# Symbolic label
text!(ax, [Point2f(r_val + ox, i_val + oy)];
text = [lbl],
fontsize = 14,
color = INK,
align = [(h, v)],
)
# Rectangular form — placed further out along the same radial direction
rect_str = i_val >= 0 ?
"$(round(r_val, digits=2))+$(round(i_val, digits=2))i" :
"$(round(r_val, digits=2))$(round(i_val, digits=2))i"
rox = r_val / mag * (0.2 + 0.24)
roy = i_val / mag * (0.2 + 0.24)
text!(ax, [Point2f(r_val + rox, i_val + roy)];
text = [rect_str],
fontsize = 10,
color = INK_SOFT,
align = [(h, v)],
)
end
# Legend (lower-left inside axis)
axislegend(ax;
position = :lb,
backgroundcolor = ELEVATED_BG,
framecolor = INK_SOFT,
labelcolor = INK,
labelsize = 12,
)
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/scatter-complex-plane/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "scatter-complex-plane",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/scatter-complex-plane/julia/makie",
"hub": "https://anyplot.ai/scatter-complex-plane",
"code_json": "https://api.anyplot.ai/specs/scatter-complex-plane/makie/code",
"spec_json": "https://api.anyplot.ai/specs/scatter-complex-plane",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/julia/makie/plot-dark.png",
"quality_score": 88.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.