论文标题
Argand的1815年“反射” - 英文翻译
Argand's "Reflexions" of 1815 -- An English Translation
论文作者
论文摘要
This is a translation from French into English of Argand's "Reflexions sur la nouvelle théorie des imaginaires, suivies d'une application à la démonstration d'un théorème d'analise", published in 1815. Argand reprises the method of representing complex numbers as points in the plane, which he first introduced in 1806. He takes up complex addition, multiplication, division, root taking, and absolute value.他给出了代数基本定理的早期，也许是第一个有效的证据，只是假设具有复杂系数的多项式的绝对值假设在复杂平面中是绝对最小值。 Argand的证明是简单而直接的，在整个19世纪，凯奇和教科书作家都将复制它的变体。
This is a translation from French into English of Argand's "Reflexions sur la nouvelle théorie des imaginaires, suivies d'une application à la démonstration d'un théorème d'analise", published in 1815. Argand reprises the method of representing complex numbers as points in the plane, which he first introduced in 1806. He takes up complex addition, multiplication, division, root taking, and absolute value. He gives an early and perhaps the first valid proof of the fundamental theorem of algebra, assuming only that the absolute value of a polynomial with complex coefficients assumes an absolute minimum in the complex plane. Argand's proof is simple and direct, variants of it being reproduced by Cauchy and textbook writers throughout the nineteenth century.
