imaginary quantity

简明释义

虚数

英英释义

例句

1.Complex numbers consist of real and imaginary quantities, which are essential in various fields of science.

复数由实数和虚数组成，这在各个科学领域都是必不可少的。

2.The concept of imaginary quantity allows engineers to work with alternating current circuits more easily.

虚数的概念使得工程师能够更轻松地处理交流电路。

3.In advanced mathematics, an imaginary quantity is often used to solve equations that do not have real solutions.

在高级数学中，虚数 常用于解决没有实数解的方程。

4.When calculating the roots of a polynomial, you may encounter an imaginary quantity if the discriminant is negative.

在计算多项式的根时，如果判别式为负，你可能会遇到虚数。

5.In physics, imaginary quantities can represent phase shifts in wave functions.

在物理学中，虚数 可以表示波函数中的相位变化。

作文

In the realm of mathematics, we often encounter various types of numbers that help us solve complex problems. One such fascinating concept is the imaginary quantity, which plays a crucial role in advanced mathematical theories and applications. To understand what an imaginary quantity is, we must first explore the concept of real numbers and their limitations.Real numbers are those that can be found on the number line, including both positive and negative values, as well as zero. However, when we try to solve equations like x² + 1 = 0, we find ourselves in a predicament because there are no real numbers that satisfy this equation. This is where imaginary quantities come into play. The solution to this equation involves the use of the square root of -1, denoted by the symbol 'i'. Thus, we define imaginary quantity as a number that can be expressed in terms of 'i', such as 3i or -2i.The introduction of imaginary quantities revolutionized mathematics, allowing for the development of complex numbers. A complex number is composed of a real part and an imaginary quantity. For example, the number 4 + 5i consists of a real part (4) and an imaginary quantity (5i). This combination enables mathematicians and scientists to work with a broader range of problems, particularly in fields such as engineering, physics, and computer science.One of the most significant applications of imaginary quantities is in electrical engineering, where alternating current (AC) circuits are analyzed using complex numbers. By representing voltage and current as complex numbers, engineers can easily compute the phase difference and impedance in AC circuits. This application highlights how imaginary quantities provide a powerful tool for solving real-world problems.Furthermore, imaginary quantities also have implications in quantum mechanics, where they are used to describe wave functions and probabilities. The ability to incorporate imaginary quantities into mathematical models allows physicists to make predictions about the behavior of particles at the quantum level, which would be impossible using only real numbers.In conclusion, the concept of imaginary quantity is not just an abstract idea confined to the pages of mathematics textbooks; it is a fundamental aspect of modern science and engineering. By extending our understanding beyond real numbers, imaginary quantities open up new avenues for exploration and innovation. As we continue to delve deeper into the mysteries of the universe, we will undoubtedly find even more applications for these intriguing mathematical constructs. Embracing the world of imaginary quantities allows us to push the boundaries of what is possible, leading to advancements that can transform our understanding of the world around us.

在数学领域，我们经常遇到各种类型的数字，这些数字帮助我们解决复杂的问题。其中一个迷人的概念是虚数，它在高级数学理论和应用中发挥着至关重要的作用。要理解什么是虚数，我们首先必须探索实数的概念及其局限性。实数是指可以在数轴上找到的数字，包括正值、负值以及零。然而，当我们尝试解决像x² + 1 = 0这样的方程时，我们发现自己陷入困境，因为没有实数可以满足这个方程。这就是虚数发挥作用的地方。这个方程的解涉及到负一的平方根，记作'i'。因此，我们将虚数定义为可以用'i'表示的数字，例如3i或-2i。虚数的引入彻底改变了数学，使得复数的发展成为可能。复数由实部和虚数组成。例如，数字4 + 5i包含一个实部（4）和一个虚数（5i）。这种组合使得数学家和科学家能够处理更广泛的问题，特别是在工程、物理和计算机科学等领域。虚数的一个重要应用是在电气工程中，交流电（AC）电路的分析使用复数来进行。通过将电压和电流表示为复数，工程师可以轻松计算交流电路中的相位差和阻抗。这一应用突显了虚数如何为解决现实世界的问题提供强大的工具。此外，虚数在量子力学中也有影响，它们用于描述波函数和概率。将虚数纳入数学模型的能力使物理学家能够预测量子层面粒子的行为，而仅使用实数是不可能的。总之，虚数的概念不仅仅是一个抽象的思想，限制于数学教科书的页面；它是现代科学和工程的一个基本方面。通过扩展我们对实数的理解，虚数为探索和创新开辟了新的途径。随着我们继续深入宇宙的奥秘，我们无疑会发现这些迷人的数学构造的更多应用。拥抱虚数的世界使我们能够突破可能性的界限，从而推动能够改变我们对周围世界理解的进步。