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Published in:
2017 | OriginalPaper | Chapter
Complex Numbers. The Fundamental Theorem of Algebra
Author : Alexander Isaev
Published in: Twenty-One Lectures on Complex Analysis
Publisher: Springer International Publishing
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The field of complex numbers, or the complex plane, denoted by $$ \mathbb{C} $$ , is just the usual Euclidean plane $$ \mathbb{R}^{2} $$ endowed with the additional operation of multiplication of vectors defined as follows: for (x1,y1) and (x2,y2) in $$ \mathbb{R}^{2} $$ let $$ (x_{1},y_{1})\cdot (x_{2},y_{2}):=(x_{1}x_{2}-y_{1}y_{2},x_{1}y_{2}+x_{2}y_{1}). $$ Notice that if y1 = 0, the above operation is simply the scaling of the vector (x2,y2) by x1.