问问 chatGPT： Complex numbers are used in various fields, each having its own specific applications. Here are some areas where complex numbers are most commonly used: Engineering: In electrical engineering, complex numbers are used to analyze AC circuits. In control engineering, complex numbers are used in the frequency domain analysis. Physics: Complex numbers are used in the study of quantum mechanics, where the square of the absolute value of a complex wave function represents the distribution of probabilities. Signal Processing: In digital signal processing and image processing, Fourier transforms are used to transition from time-domain to frequency-domain representations, and this process uses complex numbers. Mathematics: Complex numbers are used to solve equations that don’t have solutions in the real numbers, for instance, equations that require taking the square root of a negative number. They're also used in analytic functions and complex analysis, a branch of mathematics focusing on functions of complex numbers. Computer Science: Certain algorithms, particularly those dealing with graphics, use complex numbers. Fluid Dynamics: In aerodynamics, the calculation of flow around an airfoil can be calculated using complex numbers. Remember, wherever waves, oscillations, or any kind of periodic behavior is found, complex numbers are likely to be involved.
问问 chatGPT： Complex numbers are used in various fields, each having its own specific applications. Here are some areas where complex numbers are most commonly used: Engineering: In electrical engineering, complex numbers are used to analyze AC circuits. In control engineering, complex numbers are used in the frequency domain analysis. Physics: Complex numbers are used in the study of quantum mechanics, where the square of the absolute value of a complex wave function represents the distribution of probabilities. Signal Processing: In digital signal processing and image processing, Fourier transforms are used to transition from time-domain to frequency-domain representations, and this process uses complex numbers. Mathematics: Complex numbers are used to solve equations that don’t have solutions in the real numbers, for instance, equations that require taking the square root of a negative number. They're also used in analytic functions and complex analysis, a branch of mathematics focusing on functions of complex numbers. Computer Science: Certain algorithms, particularly those dealing with graphics, use complex numbers. Fluid Dynamics: In aerodynamics, the calculation of flow around an airfoil can be calculated using complex numbers. Remember, wherever waves, oscillations, or any kind of periodic behavior is found, complex numbers are likely to be involved. fridec2 发表于 2023-07-02 14:18
Complex numbers are used in various fields, each having its own specific applications. Here are some areas where complex numbers are most commonly used: Engineering: In electrical engineering, complex numbers are used to analyze AC circuits. In control engineering, complex numbers are used in the frequency domain analysis. Physics: Complex numbers are used in the study of quantum mechanics, where the square of the absolute value of a complex wave function represents the distribution of probabilities. Signal Processing: In digital signal processing and image processing, Fourier transforms are used to transition from time-domain to frequency-domain representations, and this process uses complex numbers. Mathematics: Complex numbers are used to solve equations that don’t have solutions in the real numbers, for instance, equations that require taking the square root of a negative number. They're also used in analytic functions and complex analysis, a branch of mathematics focusing on functions of complex numbers. Computer Science: Certain algorithms, particularly those dealing with graphics, use complex numbers. Fluid Dynamics: In aerodynamics, the calculation of flow around an airfoil can be calculated using complex numbers. Remember, wherever waves, oscillations, or any kind of periodic behavior is found, complex numbers are likely to be involved.
反正我一点都记不得了，所以孩子学的时候顺便学了一下
这就是定义，有什么牵强的？ 就象你的ID是caram一样。不需要去理解。
在国内读过初中的都知道这个概念吧
用大学知识去教育小学生，越教越糊涂。
这就是为了进行运算而定义的啊。楼主是要问为什么要进行给-1开根号这样的运算？一开始是为了解方程。如果没有这种运算，那遇到负数，方程就解不下去。后来复数的几何意义以及其他应用才陆续出现。楼主可以google一下复数的发明，读一下数学史。历史上的数学家也为此困惑了很久，这个概念的产生、被接受以及运算的丰富和运用的拓展是个很长的历史过程。数学史上这样的概念很多的。你可以去借这方面的书给孩子看，很有意思的
我最喜欢这个，从需求入手，为了数学的美感。
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哈哈哈，数学恩仇录的 第一个就讲这个 Cardano收了个好学生，第二轮终于KO掉Tartaglia
准确说是为了三次方程的解，而引入对复根号1的定义。楼主查Tartaglia, Cardano, del Ferro三个人的恩怨情仇就能找到为什么解三次一定要定义这个虚数单位。不过虚数的名称是笛卡尔提出的。复数的表达是达朗贝儿提出的。完美公式是欧拉提出的。最后把一些面纱解开的是高斯小王子。
高斯有关于虚数，复数，复平面通俗易懂的详细介绍，正是他，揭开了虚数的面纱。
为后来的复函数，希空间，以及物理上的波，弦奠定了基础。