This paper presents an analysis of a hitherto barely known conceptual problem in the foundations of arithmetic. An unknown type of number, so-called complex numbers, first emerged in 18th century France and became connected with the claim of non-commutativity of their multiplication. These first French practitioners are here analysed, along with examination of the impact of the introduction of the metric decimal system. International dissemination of the notion is then analysed, in particular in the case of Brazil. The paper concludes by looking at the mathematical foundations of multiplying (physical) quantities.

中文翻译：

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“复数”和数量之间的乘法问题

本文对算术基础中迄今为止鲜为人知的概念问题进行了分析。一种未知类型的数，即所谓的复数，最早出现于 18 世纪的法国，并与它们的乘法不可交换性的主张联系在一起。这里分析了这些第一批法国从业者，并考察了引入公制十进制系统的影响。然后分析这一概念的国际传播，特别是在巴西的情况下。本文最后通过研究（物理）量相乘的数学基础。