Theorem 1   If the infinite product $$\prod_{\nu=1}^\infty (1\!+\!c_\nu) = (1\!+\!c_1)(1\!+\!c_2)\cdots$$ of complex numbers $1\!+\!c_\nu$ is absolutely convergent, then its value, i.e. $\displaystyle\lim_{n\to\infty}\prod_{\nu=1}^n (1\!+\!c_\nu)$ does not depend on the order of its factors and vanishes only when some factor is zero.