book:chap2:2.4_fields
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| book:chap2:2.4_fields [2022/04/01 21:01] – jv | book:chap2:2.4_fields [2024/11/09 10:12] (current) – jv | ||
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| Line 94: | Line 94: | ||
| & = ( x_1 + \mathrm{i} y_1 ) \cdot ( x_2 + \mathrm{i} y_2 ) | & = ( x_1 + \mathrm{i} y_1 ) \cdot ( x_2 + \mathrm{i} y_2 ) | ||
| \\ | \\ | ||
| - | & = ( x_1 \, x_2 + \mathrm{i} | + | & = x_1 \, x_2 + x_1\, (\mathrm{i} |
| \\ | \\ | ||
| - | &= ( x_1\, x_2 - y_1\,y_2 ) + \mathrm{i} \, (y_1 \, x_2 + x_1 \, y_2) | + | &= ( x_1\, x_2 - y_1\,y_2 ) + \mathrm{i} \, (x_1 \, y_2 + y_1 \, x_2) |
| \end{align*} | \end{align*} | ||
| Checking the group axioms based on this representation of the complex numbers is tedious. | Checking the group axioms based on this representation of the complex numbers is tedious. | ||
book/chap2/2.4_fields.1648839660.txt.gz · Last modified: 2022/04/01 21:01 by jv