Swiftで数値計算を行う – WWDC2020

import Numerics

// 1.0, 2.0はDoubleなので、zはComplex<Double>型となる
let z = Complex(1.0, 2.0) // z = 1 + 2 i

public struct Complex<NumberType> where NumberType: Real {
    /// The real component
    public var real: NumberType
  
    /// The imaginary component
    public var imaginary: NumberType
  
    /// Construct a complex number with specified real and imaginary parts
    public init(_ real: NumberType, _ imaginary: NumberType) {
        self.real = real
        self.imaginary = imaginary
    }
}

// 算術演算の定義
extension Complex: SignedNumeric {
    /// The sum of 'z' and 'w'
    public static func +(z: Complex, w: Complex) -> Complex {
        return Complex(z.real + w.real, z.imaginary + w.imaginary)
    }

    /// The difference of 'z' and 'w'
    public static func -(z: Complex, w: Complex) -> Complex {
        return Complex(z.real - w.real, z.imaginary - w.imaginary)
    }

    /// The product of 'z' and 'w'
    public static func *(z: Complex, w: Complex) -> Complex {
        return Complex(z.real * w.real - z.imaginary * w.imaginary,
                       z.real * w.imaginary + z.imaginary * w.real)
    }
}

extension Complex {
    /// The Euclidean norm (a.k.a. 2-norm) of the number.
    public var length: NumberType {
        return .hypot(real, imaginary)
    }
  
    /// The phase (angle, or "argument").
    ///
    /// Returns the angle (measured above the real axis) in radians.
    public var phase: NumberType {
        return .atan2(y: imaginary, x: real)
    }
  
    /// A complex value with specified polar coordinates.
    public init(length: NumberType, phase: NumberType) {
        self = Complex(.cos(phase), .sin(phase)).multiplied(by: length)
    }
}