C# Complex Fast Fourier Transform

ComplexFft.cs

using System;
public class ComplexFFT
{
    public Complex[] Fft(Complex[] arr)
    {
        var length = arr.Length;
        var hLength = length >> 1;
        if (length == 1)
            return arr;
        var evenCoefficients = new Complex[hLength];
        var oddCoefficients = new Complex[hLength];
        var roots  = new Complex[length];
        var y  = new Complex[length];
        for (var i = 0; i < length; i++)
        {
            var alpha = 2 * Math.PI * i / length;
            roots[i] = new Complex(Math.Cos(alpha), Math.Sin(alpha));
        }
        for (var i = 0; i < hLength; i++)
        {
            evenCoefficients[i] = arr[i * 2];
            oddCoefficients[i] = arr[i * 2 + 1];
        }
        var evenOrderCoefficientTransform = Fft(evenCoefficients);
        var oddOrderCoefficientTransform = Fft(oddCoefficients);
        for (var i = 0; i < hLength; i++)
        {
            y[i]       = evenOrderCoefficientTransform[i] + roots[i] * oddOrderCoefficientTransform[i];
            y[i + hLength] = evenOrderCoefficientTransform[i] - roots[i] * oddOrderCoefficientTransform[i];
        }
        return y;
    }
}