use of complex number in digital signal processing
Any complex array could be represented as a real array as follows:
$$x_R = \begin{bmatrix}
 \Re(x) \\
\Im(x)
\end{bmatrix}$$
and matrices are represented as 
$$A_R = \begin{bmatrix}
 \Re(A) &amp; \Im(A) \\
-\Im(A) &amp; \Re(A)
\end{bmatrix}$$
where $\Re(x),\Im(x)$ are vectors containing the real and imaginary part of complex vector $x$, respectively. Note that addition/subtraction is preserved by simply addition 
$$x_R + y_R = z_R$$
You can also verify that matrix multiplications in the real domain also preserves the real/complex information in their respective blocks, namely
$$A_RB_R = C_R$$
where $C_R = \begin{bmatrix}
 \Re(C) &amp; \Im(C) \\
-\Im(C) &amp; \Re(C)
\end{bmatrix}$