For a complex number written in three pieces as (x, y, k) ≡ (x + iy) × 2k, write code to raise this complex number to the power −1/2. Invert the characteristic function of the normal distribution φ(t)...

For a complex number written in three pieces as (x, y, k) ≡ (x + iy) × 2k, write code to raise this complex number to the power −1/2.

Invert the characteristic function of the normal distribution φ(t) = exp{−t 2 /2} to obtain the density, using (14.7.4) and the FFT. Compare the computed density with that of the normal.