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&=& \sum_{i=1}^n (a_i^2 +b_i^2). \nonumber  \end{eqnarray}   We first look at the first element of Equation \ref{eqn:one} with $f(x) = \|x\|_{\ell_2}^2$. Thus wehave,  %Applying Equation \ref{eqn:one} with $f(x) = \|x\|_{\ell_2}^2$, we  have \begin{equation}  \frac{\partial \|x\|_{\ell_2}^2}{\partial x_i} = \frac{\partial \|x\|_{\ell_2}^2}{\partial a_i} +   j\frac{\partial \|x\|_{\ell_2}^2}{\partial b_i}. \nonumber  \end{equation}