(For c-FastICA) On covariance and pseudocovariance matrix of a complex random vector
You have

$$E[s_ks_k^*]=E[|s_k|^2]=1$$

because the complex random variables $s_k$ have zero mean and unit variance. That means that all elements of the main diagonal of $E[\mathbf{s}\mathbf{s}^H]$ equal $1$. Furthermore, with $s_k=x_k+jy_k$we have 

$$\begin{align}E[s_ks^*_l]&amp;=E[x_kx_l+y_ky_l+j(x_ly_k-x_ky_l)]\\&amp;=E[x_kx_l]+E[y_ky_l]+jE[x_ly_k]-jE[x_ky_l]\\&amp;=0,\qquad k\neq l\end{align}$$

because real and imaginary parts are uncorrelated. Consequently, all off-diagonal elements of $E[\mathbf{s}\mathbf{s}^H]$ are zero.

The off-diagonal elements of $E[\mathbf{s}\mathbf{s}^T]$ are zero for the same reason. (There's just a sign difference in the sum of the expectations, but since each of them is zero the result is the same). The main diagonal elements are 

$$\begin{align}E[s_k^2]&amp;=E[x_k^2-y_k^2+2jx_ky_k]\\&amp;=E[x_k^2]-E[y_k^2]+2jE[x_ky_k]\\&amp;=0\end{align}$$

because real and imaginary parts are uncorrelated, and they have equal variance, i.e., $E[x_k^2]=E[y_k^2]$.