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: letsplot 4.10.1 | Python 3.13.13
Quality: 87/100 | Updated: 2026-06-02
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
from lets_plot.export import ggsave as export_ggsave
LetsPlot.setup_html()
THEME = os.getenv("ANYPLOT_THEME", "light")
# Imprint palette — theme-independent, canonical order
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Theme-adaptive chrome tokens
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"
RULE = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Unit circle subtle tint using Imprint brand green
CIRCLE_ALPHA = 0.08 if THEME == "light" else 0.12
# Data — 5th roots of unity + arbitrary points + complex sum
np.random.seed(42)
n_roots = 5
roots_angles = np.array([2 * np.pi * k / n_roots for k in range(n_roots)])
roots_real = np.cos(roots_angles)
roots_imag = np.sin(roots_angles)
roots_labels = [f"ω{k}" for k in range(n_roots)]
arbitrary_real = np.array([1.8, -2.0, 0.5, -0.4, 2.3, -1.6])
arbitrary_imag = np.array([1.3, -1.4, 2.1, -1.9, -0.5, 0.7])
arbitrary_labels = [f"z{i + 1}" for i in range(len(arbitrary_real))]
sum_real = np.array([roots_real[1] + roots_real[2]])
sum_imag = np.array([roots_imag[1] + roots_imag[2]])
sum_labels = ["ω1+ω2"]
all_real = np.concatenate([roots_real, arbitrary_real, sum_real])
all_imag = np.concatenate([roots_imag, arbitrary_imag, sum_imag])
all_labels = roots_labels + arbitrary_labels + sum_labels
all_category = ["5th Root of Unity"] * n_roots + ["Arbitrary"] * len(arbitrary_real) + ["Sum"]
all_mag = np.sqrt(all_real**2 + all_imag**2)
all_angle_deg = np.degrees(np.arctan2(all_imag, all_real))
rect_labels = []
for r, i in zip(all_real, all_imag, strict=True):
sign = "+" if i >= 0 else "−"
rect_labels.append(f"{r:.2f}{sign}{abs(i):.2f}i")
polar_labels = []
for mag, ang in zip(all_mag, all_angle_deg, strict=True):
polar_labels.append(f"r={mag:.2f}, θ={ang:.0f}°")
df = pd.DataFrame(
{
"real": all_real,
"imaginary": all_imag,
"label": all_labels,
"category": all_category,
"rect_form": rect_labels,
"polar_form": polar_labels,
"magnitude": all_mag,
"angle_deg": all_angle_deg,
}
)
# Radial label placement with iterative repulsion to reduce overlap
angles = np.arctan2(all_imag, all_real)
base_offset = 0.5
label_x = all_real + base_offset * np.cos(angles)
label_y = all_imag + base_offset * np.sin(angles) + 0.2
min_sep = 0.9
for _ in range(20):
for i in range(len(label_x)):
for j in range(i + 1, len(label_x)):
dx = label_x[i] - label_x[j]
dy = label_y[i] - label_y[j]
dist = np.sqrt(dx**2 + dy**2)
if dist < min_sep:
push = 0.15 * (min_sep - dist) / max(dist, 0.01)
label_x[i] += dx * push
label_y[i] += dy * push
label_x[j] -= dx * push
label_y[j] -= dy * push
df["label_x"] = label_x
df["label_y"] = label_y
# Vectors from origin to each point
arrows_df = pd.DataFrame(
{
"x_start": np.zeros(len(all_real)),
"y_start": np.zeros(len(all_real)),
"x_end": all_real,
"y_end": all_imag,
"category": all_category,
}
)
# Unit circle path
theta = np.linspace(0, 2 * np.pi, 200)
circle_df = pd.DataFrame({"x": np.cos(theta), "y": np.sin(theta)})
# 3 categories use Imprint positions 1–3
colors = IMPRINT_PALETTE[:3]
# Tooltips for HTML interactivity — lets-plot distinctive feature
point_tooltips = (
layer_tooltips()
.title("@label")
.line("Category|@category")
.line("Rectangular|@rect_form")
.line("Polar|@polar_form")
.format("magnitude", ".3f")
.format("angle_deg", ".1f")
)
anyplot_theme = theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid_major=element_line(color=RULE, size=0.25),
panel_grid_minor=element_blank(),
axis_title=element_text(size=12, color=INK),
axis_text=element_text(size=10, color=INK_SOFT),
axis_line=element_blank(),
panel_border=element_blank(),
plot_title=element_text(size=14, color=INK, face="bold"),
plot_subtitle=element_text(size=10, color=INK_SOFT, face="italic"),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_text=element_text(size=10, color=INK_SOFT),
legend_title=element_text(size=11, color=INK),
plot_margin=[20, 35, 15, 15],
)
plot = (
ggplot()
# Unit circle filled region (subtle Imprint green tint)
+ geom_polygon(
data=circle_df,
mapping=aes(x="x", y="y"),
fill=IMPRINT_PALETTE[0],
alpha=CIRCLE_ALPHA,
color="rgba(0,0,0,0)",
)
# Dashed unit circle reference
+ geom_path(
data=circle_df,
mapping=aes(x="x", y="y"),
color=INK_SOFT,
size=0.8,
linetype="dashed",
)
# Real and imaginary axes through origin
+ geom_hline(yintercept=0, color=INK_SOFT, size=0.4)
+ geom_vline(xintercept=0, color=INK_SOFT, size=0.4)
# Vectors from origin (magnitude and phase visualization)
+ geom_segment(
data=arrows_df,
mapping=aes(
x="x_start", y="y_start", xend="x_end", yend="y_end", color="category"
),
size=1.0,
alpha=0.6,
arrow=arrow(length=10, type="open"),
)
# Points with interactive tooltips
+ geom_point(
data=df,
mapping=aes(x="real", y="imaginary", color="category"),
size=5,
alpha=0.95,
shape=21,
fill=PAGE_BG,
stroke=2.0,
tooltips=point_tooltips,
)
# Bold name labels positioned radially outward
+ geom_text(
data=df,
mapping=aes(x="label_x", y="label_y", label="label", color="category"),
size=4,
fontface="bold",
)
# Rectangular form (a+bi) below name
+ geom_text(
data=df,
mapping=aes(x="label_x", y="label_y", label="rect_form"),
size=3.5,
color=INK_SOFT,
nudge_y=-0.26,
)
+ scale_color_manual(values=colors)
+ coord_fixed()
+ labs(
x="Real Part",
y="Imaginary Part",
title="scatter-complex-plane · python · letsplot · anyplot.ai",
subtitle="5th roots of unity, arbitrary points, and complex addition on the Argand diagram",
color="Category",
)
+ scale_x_continuous(breaks=[-3, -2, -1, 0, 1, 2, 3], expand=[0.12, 0.12])
+ scale_y_continuous(breaks=[-3, -2, -1, 0, 1, 2, 3], expand=[0.12, 0.12])
# Square canvas: 600×600 × scale=4 → 2400×2400 px (equal-aspect complex plane)
+ ggsize(600, 600)
+ anyplot_theme
)
# Save PNG (scale=4 → 2400×2400 px) and interactive HTML to current directory
export_ggsave(plot, filename=f"plot-{THEME}.png", path=".", scale=4)
export_ggsave(plot, filename=f"plot-{THEME}.html", path=".")
Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.