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: seaborn 0.13.2 | Python 3.13.13
Quality: 89/100 | Updated: 2026-06-02
"""
import os
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
# Theme tokens (see prompts/default-style-guide.md "Theme-adaptive Chrome")
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 — first series always #009E73
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
sns.set_theme(
style="white",
rc={
"figure.facecolor": PAGE_BG,
"axes.facecolor": PAGE_BG,
"axes.edgecolor": INK_SOFT,
"axes.labelcolor": INK,
"text.color": INK,
"xtick.color": INK_SOFT,
"ytick.color": INK_SOFT,
"grid.color": INK,
"grid.alpha": 0.15,
"legend.facecolor": ELEVATED_BG,
"legend.edgecolor": INK_SOFT,
},
)
# Data — 3rd roots of unity, their sum, and arbitrary points across all quadrants
roots_of_unity = [np.exp(2j * np.pi * k / 3) for k in range(3)]
root_sum = sum(roots_of_unity)
arbitrary_points = [2.5 + 1.5j, -1.8 + 2.2j, 1.0 - 2.0j, -2.5 - 1.0j, 0.5 + 2.8j, -1.2 - 2.5j, 3.0 + 0.0j]
all_points = roots_of_unity + [root_sum] + arbitrary_points
labels = (
[f"$\\omega_{k}$" for k in range(3)]
+ ["$\\Sigma\\omega_k$"]
+ [f"$z_{{{i + 1}}}$" for i in range(len(arbitrary_points))]
)
categories = ["Roots of Unity"] * 3 + ["Sum of Roots"] * 1 + ["Arbitrary Points"] * len(arbitrary_points)
magnitudes = [abs(z) for z in all_points]
df = pd.DataFrame(
{
"real": [z.real for z in all_points],
"imaginary": [z.imag for z in all_points],
"label": labels,
"category": categories,
"magnitude": magnitudes,
}
)
cat_colors = {
"Roots of Unity": IMPRINT_PALETTE[0], # #009E73 green — first series
"Sum of Roots": IMPRINT_PALETTE[1], # #C475FD lavender
"Arbitrary Points": IMPRINT_PALETTE[2], # #4467A3 blue
}
markers = {"Roots of Unity": "D", "Sum of Roots": "X", "Arbitrary Points": "o"}
# JointGrid — square canvas (2400×2400 px) suits the equal-aspect complex plane
g = sns.JointGrid(data=df, x="real", y="imaginary", height=6, ratio=6, space=0.15)
g.figure.set_dpi(400)
g.figure.patch.set_facecolor(PAGE_BG)
# Main scatter with hue, style, and size encoding
sns.scatterplot(
data=df,
x="real",
y="imaginary",
hue="category",
style="category",
size="magnitude",
sizes=(150, 450),
markers=markers,
palette=cat_colors,
edgecolor=PAGE_BG,
linewidth=1.5,
zorder=5,
ax=g.ax_joint,
legend="full",
)
# Marginal KDE plots — distinctively seaborn, adds statistical context
for cat, color in cat_colors.items():
subset = df[df["category"] == cat]
sns.kdeplot(
data=subset, x="real", color=color, fill=True, alpha=0.3, linewidth=1.5, ax=g.ax_marg_x, warn_singular=False
)
sns.kdeplot(
data=subset,
y="imaginary",
color=color,
fill=True,
alpha=0.3,
linewidth=1.5,
ax=g.ax_marg_y,
warn_singular=False,
)
# Marginal axes styling
g.ax_marg_x.set_xlabel("")
g.ax_marg_x.set_ylabel("")
g.ax_marg_y.set_xlabel("")
g.ax_marg_y.set_ylabel("")
g.ax_marg_x.tick_params(left=False, labelleft=False)
g.ax_marg_y.tick_params(bottom=False, labelbottom=False)
g.ax_marg_x.set_facecolor(PAGE_BG)
g.ax_marg_y.set_facecolor(PAGE_BG)
ax = g.ax_joint
ax.set_facecolor(PAGE_BG)
# Vectors from origin to each point
for _, row in df.iterrows():
color = cat_colors[row["category"]]
ax.annotate(
"",
xy=(row["real"], row["imaginary"]),
xytext=(0, 0),
arrowprops={"arrowstyle": "->", "color": color, "lw": 1.8, "alpha": 0.5},
)
# Annotations with rectangular form — offsets in points from the data point
offsets = {
"$\\omega_0$": (20, -28),
"$\\omega_1$": (-95, -35), # lowered to clear the upper-left legend
"$\\omega_2$": (-95, -26),
"$\\Sigma\\omega_k$": (15, -55), # lower-right of origin, away from z3
"$z_{2}$": (16, -30), # below data point to avoid upper-left legend
"$z_{3}$": (45, 16), # shifted right to separate from Σωₖ annotation
"$z_{4}$": (-85, 16), # above-left to avoid ω₂ annotation in lower-left
"$z_{7}$": (-90, 16), # rightmost point — move label left to avoid right marginal
}
for _, row in df.iterrows():
r = row["real"]
i_val = row["imaginary"]
r_str = "0" if abs(r) < 0.01 else f"{r:.1f}"
if abs(i_val) < 0.01:
rect_form = f"{r_str}+0.0i"
elif i_val >= 0:
rect_form = f"{r_str}+{i_val:.1f}i"
else:
rect_form = f"{r_str}{i_val:.1f}i"
offset = offsets.get(row["label"], (16, 16))
ax.annotate(
f"{row['label']}\n{rect_form}",
xy=(r, i_val),
xytext=offset,
textcoords="offset points",
fontsize=9,
color=INK,
fontweight="medium",
bbox={
"boxstyle": "round,pad=0.3",
"facecolor": ELEVATED_BG,
"edgecolor": INK_SOFT,
"alpha": 0.9,
"linewidth": 0.5,
},
zorder=6,
)
# Equilateral triangle connecting roots of unity
root_reals = [z.real for z in roots_of_unity] + [roots_of_unity[0].real]
root_imags = [z.imag for z in roots_of_unity] + [roots_of_unity[0].imag]
ax.plot(root_reals, root_imags, ls="-", color=IMPRINT_PALETTE[0], lw=2.0, alpha=0.4, zorder=3)
# Unit circle — dashed reference at r=1
theta = np.linspace(0, 2 * np.pi, 200)
ax.plot(np.cos(theta), np.sin(theta), ls="--", color=INK_MUTED, lw=1.8, alpha=0.8, label="Unit Circle")
# Style
ax.set_aspect("equal")
title = "scatter-complex-plane · python · seaborn · anyplot.ai"
n = len(title)
title_fontsize = max(8, round(12 * (67 / n if n > 67 else 1.0)))
# Reserve top margin so suptitle sits above the top marginal without clipping
g.figure.subplots_adjust(top=0.90)
g.figure.suptitle(title, fontsize=title_fontsize, fontweight="medium", color=INK, y=0.97)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT)
ax.axhline(0, color=INK_SOFT, lw=1.0, zorder=0)
ax.axvline(0, color=INK_SOFT, lw=1.0, zorder=0)
sns.despine(ax=ax, left=True, bottom=True)
sns.despine(ax=g.ax_marg_x, left=True, bottom=True)
sns.despine(ax=g.ax_marg_y, left=True, bottom=True)
ax.xaxis.grid(True, alpha=0.15, linewidth=0.8, color=INK)
ax.yaxis.grid(True, alpha=0.15, linewidth=0.8, color=INK)
limit = 3.8
ax.set_xlim(-limit, limit)
ax.set_ylim(-limit, limit)
ax.set_xlabel("Re(z)", fontsize=10, labelpad=8, color=INK)
ax.set_ylabel("Im(z)", fontsize=10, labelpad=8, color=INK)
# Legend — keep category + unit circle entries, remove magnitude size entries
handles, leg_labels = ax.get_legend_handles_labels()
keep = []
for handle, lbl in zip(handles, leg_labels, strict=False):
if lbl not in {"magnitude", "", "category"}:
try:
float(lbl)
except ValueError:
keep.append((handle, lbl))
filtered_handles, filtered_labels = zip(*keep, strict=False) if keep else ([], [])
ax.legend(
filtered_handles,
filtered_labels,
fontsize=8,
loc="upper left",
framealpha=0.95,
edgecolor=INK_SOFT,
fancybox=True,
labelcolor=INK,
)
# Save — bbox_inches must stay default (None) to preserve exact 2400×2400 canvas
plt.savefig(f"plot-{THEME}.png", dpi=400)
Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.