Is this a kind of aliasing error and how to make correction?
Complex multiplication dictates that even a complex series with a disappearing imaginary when multiplied with a complex number:
let

$$\begin{align}
z_n &amp;= a_n + i\cdot b_n,\quad a_n, b_n \in \mathbb{R}\\
&amp;\text{then}\\
 z_1 \cdot z_2 &amp;= a_1\cdot a_2+a_1\cdot ib_2+ ib_1 \cdot ia_2 + ib_1\cdot ib_2\\
&amp;=(a_1a_2-b_1b_2) + (a_1b_2+a_2b_1)i\\
&amp;\text{let }b_1\equiv0\\
&amp;=(a_1a_2-b_1b_2) + ({a_1b_2})i
\end{align}$$

and hence, the imaginary part of $z_1$ multiplied with a complex number is not inherently zero, just because the imaginary part of $z_1$ is zero.