imaginary quantity

简明释义

虚量

英英释义

例句

1.In complex number theory, an imaginary quantity is represented as a multiple of the square root of -1.

在复数理论中，虚数表示为-1的平方根的倍数。

2.The concept of imaginary quantities allows mathematicians to solve equations that have no real solutions.

虚数的概念使数学家能够解决没有实数解的方程。

3.Engineers often deal with imaginary quantities when analyzing electrical circuits using complex impedance.

工程师在使用复阻抗分析电路时常常处理虚数。

4.In signal processing, imaginary quantities are used to represent phase shifts in sinusoidal signals.

在信号处理中，虚数用于表示正弦信号中的相位移。

5.When discussing wave functions in quantum mechanics, imaginary quantities play a crucial role.

在讨论量子力学中的波函数时，虚数起着至关重要的作用。

作文

In the realm of mathematics, particularly in complex number theory, the term imaginary quantity is of significant importance. An imaginary quantity is defined as a number that can be expressed as a real number multiplied by the imaginary unit 'i', where 'i' is the square root of -1. This concept may seem abstract at first, but it plays a crucial role in various branches of mathematics and engineering. Understanding imaginary quantities opens the door to a deeper comprehension of complex numbers and their applications.To grasp the idea of imaginary quantities, one must first familiarize themselves with the number line. On this line, we have real numbers, which can be positive, negative, or zero. However, when we venture into the world of complex numbers, we introduce a second axis, perpendicular to the real number line. This new axis represents imaginary quantities. The combination of real and imaginary quantities forms what we call complex numbers.For example, the number 3 can be represented on the real number line, while 2i, which is an imaginary quantity, would be plotted on the imaginary axis. A complex number such as 3 + 2i combines both aspects, where 3 is the real part and 2i is the imaginary quantity. This combination allows for more comprehensive mathematical operations and solutions.One of the most fascinating applications of imaginary quantities lies in electrical engineering. Alternating current (AC) circuits often utilize complex numbers to represent voltage and current. By using imaginary quantities, engineers can analyze the phase differences between these two essential elements. This analysis is vital for designing efficient electrical systems and ensuring that they operate correctly.Furthermore, imaginary quantities also appear in various fields such as physics, computer science, and even economics. In physics, for instance, the behavior of waves can be described using complex numbers, where imaginary quantities help model phenomena like interference and resonance. In computer graphics, complex numbers are employed to perform transformations and rotations, enhancing visual effects and animations.Despite their name, imaginary quantities are very much real in their applications. They may not correspond to physical quantities we can measure directly, but they provide a framework for solving problems that involve oscillatory behavior and cyclical patterns. For students and professionals alike, mastering the concept of imaginary quantities is essential for navigating the complexities of advanced mathematics and its practical applications.In conclusion, the term imaginary quantity may initially evoke confusion or skepticism due to its name, but it is a powerful concept that enriches our understanding of mathematics and its applications. Whether in engineering, physics, or computer science, imaginary quantities enable us to tackle problems that would otherwise be insurmountable. Embracing the world of complex numbers and imaginary quantities not only enhances our mathematical skills but also broadens our perspective on the interconnectedness of various scientific disciplines.

在数学领域，特别是在复数理论中，术语虚数具有重要意义。虚数被定义为可以表示为实数乘以虚数单位'i'的数字，其中'i'是-1的平方根。这个概念乍一看可能显得抽象，但它在数学和工程的各个分支中起着至关重要的作用。理解虚数为更深入地理解复数及其应用打开了大门。要理解虚数的概念，首先必须熟悉数字线。在这条线上，我们有实数，它可以是正数、负数或零。然而，当我们进入复数的世界时，我们引入了一个垂直于实数线的第二个轴。这条新轴代表虚数。实数和虚数的组合形成了我们所称的复数。例如，数字3可以在实数线上表示，而2i，作为一个虚数，将在虚数轴上绘制。像3 + 2i这样的复数结合了两个方面，其中3是实部，2i是虚数。这种组合允许更全面的数学运算和解决方案。虚数的一个最迷人的应用在于电气工程。交流电（AC）电路通常利用复数来表示电压和电流。通过使用虚数，工程师可以分析这两个基本元素之间的相位差。这种分析对于设计高效的电气系统并确保它们正常运行至关重要。此外，虚数也出现在物理学、计算机科学甚至经济学等多个领域。例如，在物理学中，波的行为可以使用复数来描述，其中虚数有助于建模干涉和共振等现象。在计算机图形学中，复数用于执行变换和旋转，从而增强视觉效果和动画。尽管名称上带有“虚”，但虚数在其应用中却非常真实。它们可能不对应于我们直接可以测量的物理量，但它们提供了一个解决涉及振荡行为和周期性模式的问题的框架。对于学生和专业人士来说，掌握虚数的概念对于应对高级数学及其实际应用的复杂性至关重要。总之，术语虚数可能因其名称而最初引起困惑或怀疑，但它是一个强大的概念，丰富了我们对数学及其应用的理解。无论是在工程、物理还是计算机科学中，虚数使我们能够解决否则无法克服的问题。接受复数和虚数的世界不仅增强了我们的数学技能，还拓宽了我们对各种科学学科相互联系的视角。