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: pygal 3.1.0 | Python 3.13.13
Quality: 83/100 | Updated: 2026-06-02
"""
import os
import numpy as np
import pygal
from pygal.style import Style
# Theme tokens (Imprint palette)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
IMPRINT_PALETTE = ("#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314")
# Data — 3rd roots of unity + sample complex numbers + vector sum
np.random.seed(42)
roots_of_unity = [np.exp(2j * np.pi * k / 3) for k in range(3)]
sample_pts = [2.5 + 1.0j, -1.8 + 1.5j, 1.0 - 2.0j, -0.5 - 1.5j]
z1, z2 = sample_pts[0], sample_pts[1]
z_sum = z1 + z2 # complex addition: parallelogram / vector sum law
# Pre-compute labels inline (no helper function)
root_labels = [
(
f"ω{k}={z.real:.1f}"
if abs(z.imag) < 1e-10
else f"ω{k}={z.imag:.1f}i"
if abs(z.real) < 1e-10
else f"ω{k}={z.real:.1f}{z.imag:+.1f}i"
)
for k, z in enumerate(roots_of_unity)
]
pt_names = ["z₁", "z₂", "z₃", "z₄"]
pt_labels = [
(
f"{n}={z.real:.1f}"
if abs(z.imag) < 1e-10
else f"{n}={z.imag:.1f}i"
if abs(z.real) < 1e-10
else f"{n}={z.real:.1f}{z.imag:+.1f}i"
)
for n, z in zip(pt_names, sample_pts, strict=False)
]
sum_label = f"z₁+z₂={z_sum.real:.1f}{z_sum.imag:+.1f}i"
# Unit circle reference points
theta = np.linspace(0, 2 * np.pi, 180)
unit_circle = [(float(np.cos(t)), float(np.sin(t))) for t in theta]
# Title — 51 chars, under 67-char baseline so default fontsize applies
title = "scatter-complex-plane · python · pygal · anyplot.ai"
title_fs = max(44, round(66 * 67 / max(len(title), 67)))
# Style
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=IMPRINT_PALETTE,
font_family="DejaVu Sans, Helvetica, Arial, sans-serif",
title_font_family="DejaVu Sans, Helvetica, Arial, sans-serif",
title_font_size=title_fs,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
value_label_font_size=36,
stroke_width=2.5,
opacity=0.94,
opacity_hover=1.0,
)
# Chart — square canvas ensures equal aspect ratio for the Argand diagram
chart = pygal.XY(
width=2400,
height=2400,
style=custom_style,
title=title,
x_title="Real Axis",
y_title="Imaginary Axis",
show_legend=True,
legend_at_bottom=True,
legend_at_bottom_columns=3,
legend_box_size=24,
stroke=False,
dots_size=12,
show_x_guides=True,
show_y_guides=True,
truncate_legend=-1,
margin_bottom=140,
margin_left=100,
margin_right=80,
margin_top=100,
range=(-3.5, 3.5),
xrange=(-3.5, 3.5),
print_values=False,
print_labels=True,
js=[],
)
# Series 1: Roots of Unity (3rd) — Imprint #009E73
roots_series = []
for i, z in enumerate(roots_of_unity):
roots_series += [
{"value": (0.0, 0.0), "label": ""},
{"value": (float(z.real), float(z.imag)), "label": root_labels[i]},
None,
]
chart.add(
"Roots of Unity (3rd)",
roots_series,
stroke=True,
show_dots=True,
dots_size=20,
stroke_style={"width": 5, "linecap": "round", "opacity": 0.88},
)
# Series 2: Sample Points — Imprint #C475FD
pt_series = []
for i, z in enumerate(sample_pts):
pt_series += [
{"value": (0.0, 0.0), "label": ""},
{"value": (float(z.real), float(z.imag)), "label": pt_labels[i]},
None,
]
chart.add(
"Sample Points",
pt_series,
stroke=True,
show_dots=True,
dots_size=16,
stroke_style={"width": 3.5, "linecap": "round", "opacity": 0.75},
)
# Series 3: Vector Sum z₁+z₂ — Imprint #4467A3 (dashed = result of addition)
chart.add(
"z₁+z₂ (Vector Sum)",
[{"value": (0.0, 0.0), "label": ""}, {"value": (float(z_sum.real), float(z_sum.imag)), "label": sum_label}],
stroke=True,
show_dots=True,
dots_size=22,
stroke_style={"width": 6, "dasharray": "10, 5", "linecap": "round", "opacity": 0.92},
)
# Series 4: Unit Circle — Imprint #BD8233, subtle dashed reference
chart.add(
"Unit Circle",
unit_circle,
stroke=True,
show_dots=False,
fill=False,
stroke_style={"width": 2.5, "dasharray": "6, 6", "opacity": 0.40},
)
# Series 5: Origin — Imprint #AE3030, drawn last to render on top of all vectors
chart.add("Origin", [{"value": (0.0, 0.0), "label": ""}], stroke=False, dots_size=20)
# Save
chart.render_to_png(f"plot-{THEME}.png")
with open(f"plot-{THEME}.html", "wb") as f:
f.write(chart.render())
Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.