Complex

pub fn Complex(comptime T: type) type {
    return struct {
        const Self = @This();

        /// Real part.
        re: T,

        /// Imaginary part.
        im: T,

        /// Create a new Complex number from the given real and imaginary parts.
        pub fn init(re: T, im: T) Self {
            return Self{
                .re = re,
                .im = im,
            };
        }

        /// Returns the sum of two complex numbers.
        pub fn add(self: Self, other: Self) Self {
            return Self{
                .re = self.re + other.re,
                .im = self.im + other.im,
            };
        }

        /// Returns the subtraction of two complex numbers.
        pub fn sub(self: Self, other: Self) Self {
            return Self{
                .re = self.re - other.re,
                .im = self.im - other.im,
            };
        }

        /// Returns the product of two complex numbers.
        pub fn mul(self: Self, other: Self) Self {
            return Self{
                .re = self.re * other.re - self.im * other.im,
                .im = self.im * other.re + self.re * other.im,
            };
        }

        /// Returns the quotient of two complex numbers.
        pub fn div(self: Self, other: Self) Self {
            const re_num = self.re * other.re + self.im * other.im;
            const im_num = self.im * other.re - self.re * other.im;
            const den = other.re * other.re + other.im * other.im;

            return Self{
                .re = re_num / den,
                .im = im_num / den,
            };
        }

        /// Returns the complex conjugate of a number.
        pub fn conjugate(self: Self) Self {
            return Self{
                .re = self.re,
                .im = -self.im,
            };
        }

        /// Returns the negation of a complex number.
        pub fn neg(self: Self) Self {
            return Self{
                .re = -self.re,
                .im = -self.im,
            };
        }

        /// Returns the product of complex number and i=sqrt(-1)
        pub fn mulbyi(self: Self) Self {
            return Self{
                .re = -self.im,
                .im = self.re,
            };
        }

        /// Returns the reciprocal of a complex number.
        pub fn reciprocal(self: Self) Self {
            const m = self.re * self.re + self.im * self.im;
            return Self{
                .re = self.re / m,
                .im = -self.im / m,
            };
        }

        /// Returns the magnitude of a complex number.
        pub fn magnitude(self: Self) T {
            return @sqrt(self.re * self.re + self.im * self.im);
        }

        pub fn squaredMagnitude(self: Self) T {
            return self.re * self.re + self.im * self.im;
        }
    };
}