From ef1cdbc0c7e3ff4ef6a61bb292ca29a7d5f44471 Mon Sep 17 00:00:00 2001
From: "Yukihiro \"Matz\" Matsumoto" <matz@ruby.or.jp>
Date: Tue, 17 Jun 2025 16:19:44 +0900
Subject: [PATCH] mruby-complex: add README.md

The document is written by Google Jules.
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+# mruby-complex
+
+mruby-complex is an mrbgem that provides a `Complex` class for mruby, allowing for the representation and manipulation of complex numbers. It is designed to be compatible with the Complex class in standard Ruby.
+
+## Functionality
+
+The `Complex` class provided by this mrbgem supports:
+
+- Creation of complex numbers from real and imaginary parts, or using the `i` suffix for numbers.
+- Basic arithmetic operations: addition (`+`), subtraction (`-`), multiplication (`*`), division (`/`).
+- Methods to access the real and imaginary parts (`real`, `imaginary` or `imag`).
+- Calculation of absolute value (`abs`, `magnitude`), argument/angle (`arg`, `angle`, `phase`), and square of the absolute value (`abs2`).
+- Complex conjugate (`conjugate`, `conj`).
+- Conversion to polar coordinates (`polar`).
+- Conversion to other numeric types where appropriate (`to_f`, `to_i`, `to_r`, `to_c`).
+- Inspection and string representation (`inspect`, `to_s`).
+
+## Usage Examples
+
+Here are some basic examples of how to use the `Complex` class:
+
+```ruby
+# Creating complex numbers
+c1 = Complex(1, 2)      # => (1+2i)
+c2 = 3 + 4i             # => (3+4i)
+c3 = Complex.polar(5, Math::PI/2) # => (0.0+5.0i) (approximately)
+
+# Arithmetic operations
+puts c1 + c2  # => (4+6i)
+puts c1 - c2  # => (-2-2i)
+puts c1 * c2  # => (-5+10i)
+puts c1 / c2  # => (0.44+0.08i)
+
+# Accessing parts
+puts c1.real      # => 1
+puts c1.imaginary # => 2
+
+# Other methods
+puts c2.abs       # => 5.0
+puts c2.arg       # => 0.9272952180016122 (radians)
+puts c2.conjugate # => (3-4i)
+puts c1.polar     # => [2.23606797749979, 1.1071487177940904]
+
+# Numerics can be converted to Complex
+puts 5.to_c       # => (5+0i)
+puts 2.3.to_c     # => (2.3+0i)
+
+# The `i` method on numerics creates a complex number with zero real part
+puts 5i           # => (0+5i)
+puts 2.3i         # => (0+2.3i)
+```
+
+## Note
+
+This mrbgem aims to provide functionality similar to the `Complex` class found in the standard Ruby library. Refer to the Ruby documentation for `Complex` for more detailed information on the behavior of various methods.