complex number

简明释义

复数

英英释义

例句

1.In electrical engineering, a complex number (复数) is used to represent the impedance of a circuit.

在电气工程中，复数用于表示电路的阻抗。

2.The solution to many quadratic equations involves complex numbers (复数).

许多二次方程的解涉及到复数。

3.The complex number (复数) plane is a two-dimensional space used to visualize complex functions.

复数平面是一个二维空间，用于可视化复数函数。

4.When studying vibrations, engineers often use complex numbers (复数) to simplify calculations.

在研究振动时，工程师常常使用复数来简化计算。

5.In signal processing, complex numbers (复数) are essential for representing waveforms.

在信号处理中，复数对于表示波形是必不可少的。

作文

In the world of mathematics, numbers are not just limited to the real numbers we use in our daily lives. One fascinating category of numbers is known as complex number, which expands our understanding of numerical systems. A complex number is defined as a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, representing the square root of -1. This concept may initially seem abstract, but it has profound implications in various fields such as engineering, physics, and even finance.The introduction of complex numbers revolutionized mathematics by allowing for solutions to equations that would otherwise have no real solutions. For instance, consider the equation x² + 1 = 0. In the realm of real numbers, there is no solution since no real number squared will yield a negative result. However, by utilizing complex numbers, we find that the solutions are x = i and x = -i. This ability to solve such equations opens up new avenues for exploration in mathematics.Moreover, complex numbers are not merely theoretical constructs; they have practical applications in various scientific disciplines. In electrical engineering, for example, complex numbers are used to analyze alternating current (AC) circuits. The impedance of a circuit can be represented as a complex number, allowing engineers to calculate voltage and current more efficiently. The use of complex numbers simplifies the calculations involved in AC circuit analysis, making it easier to design and optimize electrical systems.In physics, complex numbers are also prevalent, particularly in quantum mechanics. The wave function, which describes the quantum state of a particle, is often represented using complex numbers. This representation allows physicists to capture both the amplitude and phase of a wave, providing a complete description of the quantum behavior of particles. Without complex numbers, many phenomena in quantum mechanics would be difficult, if not impossible, to describe accurately.Furthermore, complex numbers have found their way into the realm of computer graphics. They are utilized in algorithms for rendering images and simulating physical phenomena. The manipulation of complex numbers enables graphic designers and animators to create stunning visual effects and realistic simulations, enhancing the quality of digital media.In conclusion, the concept of complex numbers is not only a mathematical curiosity but also a powerful tool that enhances our understanding of the universe. From solving equations that lack real solutions to facilitating advancements in engineering, physics, and computer graphics, complex numbers play a crucial role in the modern world. As we continue to explore the depths of mathematics and its applications, the significance of complex numbers will undoubtedly grow, further bridging the gap between abstract theory and practical implementation. Embracing the beauty and utility of complex numbers can lead to a deeper appreciation of the intricate tapestry of mathematics that underpins so much of our technological advancements today.

在数学的世界中，数字不仅限于我们日常生活中使用的实数。有一个迷人的数字类别被称为复数，它扩展了我们对数字系统的理解。复数定义为可以表示为a + bi的数字，其中'a'和'b'是实数，'i'是虚单位，表示-1的平方根。这个概念最初可能看起来很抽象，但它在工程、物理甚至金融等各个领域都有深远的影响。复数的引入通过允许解决那些在实数范围内没有解的方程式，彻底改变了数学。例如，考虑方程x² + 1 = 0。在实数的领域中，没有解决方案，因为没有实数的平方会产生负结果。然而，通过利用复数，我们发现解为x = i和x = -i。这种解决此类方程的能力为数学探索开辟了新的途径。此外，复数并不仅仅是理论构造；它们在各种科学学科中具有实际应用。例如，在电气工程中，复数用于分析交流（AC）电路。电路的阻抗可以表示为复数，这使得工程师能够更高效地计算电压和电流。使用复数简化了交流电路分析中的计算，使设计和优化电气系统变得更加容易。在物理学中，复数也很普遍，尤其是在量子力学中。描述粒子量子态的波函数通常使用复数表示。这种表示方法使物理学家能够捕捉波的幅度和相位，从而提供对粒子量子行为的完整描述。如果没有复数，许多量子力学现象将难以准确描述，甚至不可能描述。此外，复数还进入了计算机图形学的领域。它们被用于渲染图像和模拟物理现象的算法中。对复数的操作使图形设计师和动画师能够创建惊人的视觉效果和逼真的模拟，从而增强数字媒体的质量。总之，复数的概念不仅是数学的好奇心，也是增强我们对宇宙理解的强大工具。从解决缺乏实数解的方程到促进工程、物理和计算机图形学的进步，复数在现代世界中发挥着至关重要的作用。随着我们继续探索数学及其应用的深度，复数的重要性无疑会增长，进一步弥合抽象理论与实际应用之间的差距。接受复数的美丽和实用性，可以让我们更深刻地欣赏支撑我们今天许多技术进步的数学复杂织锦。