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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 82/100 | Created: 2026-06-02
library(ggplot2)
library(ragg)
# Theme tokens
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
IMPRINT_PALETTE <- c(
"#009E73", # 1 — brand green (5th roots of unity)
"#C475FD", # 2 — lavender (arbitrary points)
"#4467A3", # 3 — blue
"#BD8233", # 4 — ochre
"#AE3030", # 5 — matte red
"#2ABCCD", # 6 — cyan
"#954477", # 7 — rose
"#99B314" # 8 — lime
)
GRID_COLOR <- adjustcolor(INK, alpha.f = 0.12)
# Data: 5th roots of unity (z^5 = 1, evenly spaced on the unit circle)
n <- 5
angles <- 2 * pi * (0:(n - 1)) / n
unity_real <- cos(angles)
unity_imag <- sin(angles)
# Rectangular form labels: a + bi (inlined)
unity_labels <- mapply(
function(r, i) if (i >= 0) sprintf("%.2f + %.2fi", r, i) else sprintf("%.2f - %.2fi", r, abs(i)),
unity_real, unity_imag
)
# Two arbitrary complex numbers outside the unit circle
arb_real <- c( 1.30, -0.60)
arb_imag <- c( 0.70, -1.40)
arb_angles <- atan2(arb_imag, arb_real)
arb_labels <- mapply(
function(r, i) if (i >= 0) sprintf("%.2f + %.2fi", r, i) else sprintf("%.2f - %.2fi", r, abs(i)),
arb_real, arb_imag
)
# Combined data frame
df <- data.frame(
real = c(unity_real, arb_real),
imag = c(unity_imag, arb_imag),
label = c(unity_labels, arb_labels),
angle = c(angles, arb_angles),
category = factor(
c(rep("5th Roots of Unity", n), rep("Arbitrary Points", 2)),
levels = c("5th Roots of Unity", "Arbitrary Points")
),
stringsAsFactors = FALSE
)
# Nudge labels outward from origin for readability
nudge_scale <- 0.30
df$nx <- cos(df$angle) * nudge_scale
df$ny <- sin(df$angle) * nudge_scale
# Per-point hjust: left-align rightward labels so text clears the arrowhead
df$hjust <- ifelse(cos(df$angle) > 0.8, 0, ifelse(cos(df$angle) < -0.8, 1, 0.5))
# Unit circle reference path
theta_seq <- seq(0, 2 * pi, length.out = 300)
circle_df <- data.frame(x = cos(theta_seq), y = sin(theta_seq))
# Title (48 chars — below 67-char baseline, no font shrink needed)
title_str <- "scatter-complex-plane · r · ggplot2 · anyplot.ai"
title_size <- max(8, round(12 * 67 / max(nchar(title_str), 67)))
category_colors <- c(
"5th Roots of Unity" = IMPRINT_PALETTE[1],
"Arbitrary Points" = IMPRINT_PALETTE[2]
)
p <- ggplot() +
# Unit circle (dashed reference)
geom_path(
data = circle_df, aes(x = x, y = y),
color = INK_SOFT, linetype = "dashed", linewidth = 0.5
) +
# Origin axes (horizontal and vertical lines through 0)
geom_hline(yintercept = 0, color = INK_SOFT, linewidth = 0.5) +
geom_vline(xintercept = 0, color = INK_SOFT, linewidth = 0.5) +
# Vectors: arrows from origin to each complex number
geom_segment(
data = df,
aes(x = 0, y = 0, xend = real, yend = imag, color = category),
arrow = arrow(length = unit(0.12, "inches"), type = "closed"),
linewidth = 0.9,
alpha = 0.85
) +
# Points
geom_point(
data = df,
aes(x = real, y = imag, color = category),
size = 3.5
) +
# Labels: rectangular form (a + bi), nudged outward from origin
geom_text(
data = df,
aes(x = real + nx, y = imag + ny, label = label, color = category, hjust = hjust),
size = 3.2,
show.legend = FALSE
) +
scale_color_manual(values = category_colors, name = NULL) +
coord_equal(xlim = c(-2.1, 2.1), ylim = c(-2.1, 2.1)) +
labs(
title = title_str,
x = "Real",
y = "Imaginary"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = GRID_COLOR, linewidth = 0.3),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = title_size, face = "bold"),
legend.background = element_rect(fill = ELEVATED_BG, color = INK_SOFT, linewidth = 0.3),
legend.text = element_text(color = INK_SOFT, size = 8),
legend.position = "bottom",
plot.margin = margin(t = 20, r = 20, b = 20, l = 20)
)
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 6,
height = 6,
units = "in",
dpi = 400
)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/scatter-complex-plane/ggplot2/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": "r",
"library": "ggplot2",
"page": "https://anyplot.ai/scatter-complex-plane/r/ggplot2",
"hub": "https://anyplot.ai/scatter-complex-plane",
"code_json": "https://api.anyplot.ai/specs/scatter-complex-plane/ggplot2/code",
"spec_json": "https://api.anyplot.ai/specs/scatter-complex-plane",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/r/ggplot2/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/scatter-complex-plane/r/ggplot2/plot-dark.png",
"quality_score": 82.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Complex Plane Visualization (Argand Diagram) on anyplot.ai.