MDSComplexNumbers

A lightweight Swift framework providing complex number support with clean syntax, stable math functions, and a Swift-friendly API. Designed for numerical work, graphics, and fractal math on iOS, iPadOS, and macOS.

Features

• Complex type with full arithmetic support
• Stable magnitude computation using hypot
• Human-readable formatting (2.00 - 0.50𝒊, 𝒊, -𝒊)
• Mixed Double + Complex arithmetic
• Immutable and consistent complex rectangles (ComplexRect)
• Fully @inlinable for performance-critical code
• Sendable, Equatable, and Hashable support

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Installation

Add MDSComplexNumbers.framework to your Xcode project binaries, then import the module where needed:

import MDSComplexNumbers

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Functions & Examples

Initialize / Create a Complex Number

var z = Complex()                 // 0.00
var w = Complex(2.5, -4.5)        // 2.50 - 4.50𝒊

z = Complex(1.1, 0.9)             // 1.10 + 0.90𝒊

var u = Complex(0, -1)            // -𝒊
u = Complex(0, 1)                 // 𝒊

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Complex Arithmetic

let sum = z + w                   // 3.60 - 3.60𝒊
let product = z * w               // 6.80 - 2.70𝒊
let squared = sqr(z)              // 0.40 + 1.98𝒊

print(z - w)                      // -1.40 + 5.40𝒊

let quotient = z / w              // 0.05 + 0.27𝒊

let areEqual = (z == w)           // false
let notEqual = (z != w)           // true

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Magnitude / Modulus

let m1 = modulus(z)               // 1.42126704035519
let m2 = z.magnitude              // same as modulus(z)
let m3 = z.modulusSquared         // avoids sqrt

Magnitude uses hypot(real, imaginary) for improved numerical stability.

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Mixed Real and Complex Arithmetic

Double as the Left Operand

let aDouble = Double.pi

print(aDouble * w)                // 7.85 - 14.14𝒊
print(aDouble + z)                // 4.24 + 0.90𝒊
print(aDouble - w)                // 0.64 + 4.50𝒊

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ComplexRect

ComplexRect represents a rectangular region in the complex plane.
Corners are always normalized and internally consistent.

let r = ComplexRect(
    Complex(-2.0, 1.0),
    Complex(1.0, -1.0)
)

r.topLeft        // -2.00 + 1.00𝒊
r.bottomRight    // 1.00 - 1.00𝒊
r.bottomLeft     // -2.00 - 1.00𝒊
r.topRight       // 1.00 + 1.00𝒊

r.width          // 3.0
r.height         // 2.0

An optional MutableComplexRect is also included if mutation is required.

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Notes

• Division by 0 + 0𝒊 triggers a runtime precondition failure.
• Formatting is intended for debugging and display, not serialization.
• The API favors correctness, clarity, and performance over cleverness.

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License

© 2018-2026 Michael Stebel Consulting, LLC. All rights reserved.