Complex(3)

✨ NAME ✨

okay so bestie, this is literally Complex from the OCaml library 💖 and it is about Complex numbers. no cap, that is the whole name vibe. we are keeping every single detail, periodt.

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🎀 Module 🎀

the module is literally Module Complex, and its signature opens with : sig end — that is the whole shape of it, bestie 🫶.

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💖 Documentation 💖

Complex numbers. this module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (cartesian representation). each part is represented by a double-precision floating-point number (type float). slay, that is the whole setup ✨.

the type is giving record realness:

type t = {
 re : float ;
 im : float ;
 }

this is the type of complex numbers. re is the real part and im is the imaginary part. iconic little pair, no notes 💅.

• val zero : t — the complex number 0. 🍓
• val one : t — the complex number 1. 🌸
• val i : t — the complex number i. 🦋
• val neg : t -> t — unary negation. 🙈
• val conj : t -> t — conjugate: given the complex x + i.y, returns x - i.y. 💫
• val add : t -> t -> t — addition. ➕
• val sub : t -> t -> t — subtraction. ➖
• val mul : t -> t -> t — multiplication. ✖️
• val inv : t -> t — multiplicative inverse (1/z). 🔄
• val div : t -> t -> t — division. ➗
• val sqrt : t -> t — square root. the result x + i.y is such that x > 0 or x = 0 and y >= 0. this function has a discontinuity along the negative real axis. ⚠️
• val norm2 : t -> float — norm squared: given x + i.y, returns x^2 + y^2. 🔥
• val norm : t -> float — norm: given x + i.y, returns sqrt(x^2 + y^2). 🌈
• val arg : t -> float — argument. the argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. this angle ranges from -pi to pi. this function has a discontinuity along the negative real axis. ⭐
• val polar : float -> float -> t — polar norm arg returns the complex having norm norm and argument arg. 🎀
• val exp : t -> t — exponentiation. exp z returns e to the z power. 👑
• val log : t -> t — natural logarithm (in base e). 🌿
• val pow : t -> t -> t — power function. pow z1 z2 returns z1 to the z2 power. 💥

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okay that is the whole page bestie — source/version is OCamldoc, date is 2026-06-22, and the page is Complex(3). mwah 💋✨