SOLVED/ 【复数10】有没有快速理解【这个如此美丽图形】的办法？

dodonaomikiki

图片【见图】注释
Domain coloring of the complex function.
Phase is coded by the hue and module by the value




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以下是关于文字旁注，关于【复数の可视化】
When visualizing complex functions, a complex input and output are both needed. Because each complex number is represented in two dimensions, visually graphing a complex function with both the input and output would require perception of four dimensional space, which is impossible. Because of this, other ways of visualizing complex functions have been designed.

In Domain coloring, the third and fourth dimensions can instead be represented by color and brightness, typically with color representing the angle of the complex number in polar form and brightness representing the magnitude. These plots are called color wheel graphs. This provides a simple way to visualize the functions without losing information.

Riemann surfaces are another way to visualize complex functions. Riemann surfaces can be thought of as deformations of the complex plane; while the horizontal axes represent the real and imaginary inputs, the single vertical axis only represents either the real or imaginary output. However, Riemann surfaces are built in such a way that rotating them 180 degrees shows the imaginary output, and vice versa. Unlike domain coloring, Riemann surfaces can represent multivalued functions like   √z




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以下是：过往历史の简短回顾
The solution in radicals (without trigonometric functions) of a general cubic equation contains the square roots of negative numbers when all three roots are real numbers, a situation that cannot be rectified by factoring aided by the rational root test if the cubic is irreducible (the so-called casus irreducibilis). This conundrum led Italian mathematician Gerolamo Cardano to conceive of complex numbers in around 1545,[16] though his understanding was rudimentary.

Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root.

Many mathematicians contributed to the full development of complex numbers. The rules for addition, subtraction, multiplication, and division of complex numbers were developed by the Italian mathematician Rafael Bombelli.[17] A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions.

dodonaomikiki

Français : Coloration de régions de la fonction complexe   f(x). La couleur (teinte) représente l'argument de la fonction. Les lignes noires et blanches (saturation, valeur) représentent les valeurs de la fonction à module constant. Ce fichier comporte 4 calques : les lignes blanches indiquant les lignes iso-argument tous les pi/6, la grille transformée du plan complexe, les variations d'intensité représentant le module, la couleur représentant l'argument
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以上，是对图形的法文注释！
因为更为详细，所以一并拿过来！说不定，坛子里有懂法文地~~~可惜我不懂，否则，我就把这一段翻译出来

drc2000再来

******这里是必须的但不漂亮的占位符号*****

drc2000再来

订正如下，180应该改为360度，后面计算也应该做做相应的变动。
但图像中的五个零点不用动

dodonaomikiki

搞出五点

dodonaomikiki

为啦简化计算，我取√2=意思意思

dodonaomikiki

Sir William Rowan Hamilton (1805–1865)
纪念一下这位老大！为复数做出巨大贡献，尤其在四元数上面
哈密顿工作勤奋，思想活跃．
哈密顿经常不能正规用餐，而是边吃边工作．他去世后，在他的论文手稿中找到不少肉骨头和吃剩的三明治等残物。