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: matplotlib 3.10.9 | Python 3.13.13
Quality: 89/100 | Created: 2026-06-02
"""
import sys
sys.path.pop(0) # prevent this file from shadowing the matplotlib package
import os
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.lines import Line2D
from matplotlib.patches import Arc
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — 8 hues, canonical order
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
COLOR_ROOTS = IMPRINT_PALETTE[0] # brand green — 5th roots of unity
COLOR_ARBIT = IMPRINT_PALETTE[1] # lavender — arbitrary complex numbers
# Data — 5th roots of unity (z^5 = 1) plus two arbitrary complex numbers
n_roots = 5
roots = [np.exp(2j * np.pi * k / n_roots) for k in range(n_roots)]
arbitrary = [1.6 + 0.7j, -0.4 + 1.5j]
labels_roots = ["1", "ω", "ω²", "ω³", "ω⁴"]
labels_arbit = ["z₁", "z₂"]
all_points = roots + arbitrary
all_labels = labels_roots + labels_arbit
all_colors = [COLOR_ROOTS] * n_roots + [COLOR_ARBIT] * len(arbitrary)
all_markers = ["o"] * n_roots + ["D"] * len(arbitrary)
# Plot — square canvas required so the unit circle appears circular
fig, ax = plt.subplots(figsize=(6, 6), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)
ax.set_aspect("equal")
# Unit circle — dashed geometric reference
theta = np.linspace(0, 2 * np.pi, 400)
ax.plot(np.cos(theta), np.sin(theta), color=INK_MUTED, linewidth=1.5, linestyle="--", alpha=0.7, zorder=1)
# Real and imaginary axes through the origin
ax.axhline(0, color=INK_SOFT, linewidth=0.9, alpha=0.6, zorder=1)
ax.axvline(0, color=INK_SOFT, linewidth=0.9, alpha=0.6, zorder=1)
# Subtle grid for both axes
ax.xaxis.grid(True, alpha=0.12, linewidth=0.6, color=INK, zorder=0)
ax.yaxis.grid(True, alpha=0.12, linewidth=0.6, color=INK, zorder=0)
# Arrows from origin to each complex number
for z, color in zip(all_points, all_colors, strict=False):
ax.annotate(
"",
xy=(z.real, z.imag),
xytext=(0.0, 0.0),
arrowprops={"arrowstyle": "->", "color": color, "lw": 1.8, "mutation_scale": 18, "shrinkA": 0, "shrinkB": 7},
zorder=3,
)
# Angle arcs — dotted arcs from positive real axis to each vector, showing the argument
for z, color in zip(all_points, all_colors, strict=False):
angle_deg = np.degrees(np.angle(z)) # in [-180, 180]
if abs(angle_deg) > 0.5:
arc = Arc(
(0, 0),
0.38,
0.38,
angle=0,
theta1=min(0.0, angle_deg),
theta2=max(0.0, angle_deg),
color=color,
linewidth=0.9,
linestyle=":",
alpha=0.45,
zorder=2,
)
ax.add_patch(arc)
# Scatter points
for z, color, marker in zip(all_points, all_colors, all_markers, strict=False):
ax.scatter(z.real, z.imag, s=130, color=color, marker=marker, edgecolors=PAGE_BG, linewidth=1.2, zorder=5)
# Labels — name, rectangular form (a+bi), and polar form (|z|∠θ°), offset outward from origin
for z, label in zip(all_points, all_labels, strict=False):
re, im = z.real, z.imag
mag = abs(z) + 1e-12
angle_deg = np.degrees(np.angle(z)) % 360
if abs(im) < 1e-10:
coord = f"{re:.2f}"
elif im >= 0:
coord = f"{re:.2f}+{im:.2f}i"
else:
coord = f"{re:.2f}{im:.2f}i"
polar = f"{abs(z):.2f}∠{angle_deg:.1f}°"
dx = (re / mag) * 0.45
dy = (im / mag) * 0.45
ax.annotate(
f"{label}\n{coord}\n{polar}",
xy=(re, im),
xytext=(re + dx, im + dy),
fontsize=9,
color=INK,
ha="center",
va="center",
bbox={"facecolor": ELEVATED_BG, "edgecolor": "none", "alpha": 0.88, "pad": 3},
zorder=6,
)
# Style
title = "scatter-complex-plane · python · matplotlib · anyplot.ai"
n_chars = len(title)
ratio = 67 / n_chars if n_chars > 67 else 1.0
title_fontsize = max(8, round(12 * ratio))
ax.set_title(title, fontsize=title_fontsize, fontweight="medium", color=INK, pad=10)
ax.set_xlabel("Real axis", fontsize=10, color=INK)
ax.set_ylabel("Imaginary axis", fontsize=10, color=INK)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_color(INK_SOFT)
ax.spines["bottom"].set_color(INK_SOFT)
ax.set_xlim(-2.4, 2.4)
ax.set_ylim(-2.4, 2.4)
# Legend
legend_elements = [
Line2D(
[0],
[0],
marker="o",
color="w",
markerfacecolor=COLOR_ROOTS,
markersize=9,
label="5th roots of unity (ω = e^(2πi/5))",
),
Line2D(
[0], [0], marker="D", color="w", markerfacecolor=COLOR_ARBIT, markersize=9, label="Arbitrary complex numbers"
),
Line2D([0], [0], color=INK_MUTED, linewidth=1.5, linestyle="--", label="Unit circle |z| = 1"),
]
leg = ax.legend(handles=legend_elements, fontsize=8, loc="lower left", framealpha=0.9)
leg.get_frame().set_facecolor(ELEVATED_BG)
leg.get_frame().set_edgecolor(INK_SOFT)
plt.setp(leg.get_texts(), color=INK_SOFT)
# Save
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)
plt.close()
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/scatter-complex-plane/matplotlib/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": "python",
"library": "matplotlib",
"page": "https://anyplot.ai/scatter-complex-plane/python/matplotlib",
"hub": "https://anyplot.ai/scatter-complex-plane",
"code_json": "https://api.anyplot.ai/specs/scatter-complex-plane/matplotlib/code",
"spec_json": "https://api.anyplot.ai/specs/scatter-complex-plane",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/python/matplotlib/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/python/matplotlib/plot-dark.png",
"quality_score": 89.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.