Complex Number

中南大学高级程序设计实践（C++）课程设计报告题目复数计算器学生姓名曾立弘指导教师陈丽萍学院信息科学与工程学院专业班级电子信息工程 1401 班完成时间2015年6月8日星期一目录第一章需求分析 (1)第二章概要设计 (2)第三章详细设计 (4)第四章调试分析 (21)第五章测试结果 (25)第六章课程设计总结 (36)第七章参考文献 (37)第八章附录 (37)第一章需求分析1.1程序设计的任务1．1.1编程目的1.本次程序设计的目的运用面向对象程序设计知识，利用C++语言设计和实现一个复数计算器，要求具备如下主要功能：（1）建立实数类、复数类（2）实现实数、复数信息的初始化（3）实现实数的加、减、乘、除、自增、自减、求平方、二次方根等操作（4）实现复数的加、减、乘、除、取模、求平方、求共轭复数、求单个复数的向量角、求两个复数的夹角等运算（5）实现实数、复数信息的输出1.1.2编程要求在实现过程中，需利用面向对象程序设计理论的基础知识，充分体现出C++语言关于类、继承、封装与多态等核心概念，每一个类应包含数据成员和成员函数。

1.1.3数据范围数据输入的形式为float型，输出形式亦是float型，数据（实数、复数的实部、虚部）范围是-2^128 ~ +2^128，也即-3.40E+38 ~ +3.40E+38。

1.2本程序能实现的功能1.2.1实数类（Complex）所实现的功能：实数的加法运算、减法运算、乘法运算、除法运算、前置自增运算、后置自增运算、前置自减运算、后置自减运算、求平方运算、求平方根运算；1.2.2复数类（Complex1）所实现的功能：复数的加法运算、减法运算、乘法运算、除法运算、模长运算、求平方运算、共轭复数运算、求单个复数的向量角运算、求两个复数的夹角运算。

1.2.3主函数所能实现的功能1.提供给操作者操作数据的类型（实数还是复数）的标识；2.操作者选择数据类型后，提供运算类型操作的标识；3.运用指针调用两个类的各成员函数分别完成各项计；第二章概要设计2.1构成部分2.1.1系统由三部分构成：实数类（Complex）、复数类（Complex1）、主函数main。

:2+2 4
:_
We typed 2 + 2, a particular example from the general class of expressions. Mata responded with 4, the evaluation of the expression.
Often what you type are expressions, although you will probably choose more complicated examples. When an expression is not assigned to a variable, the result of the expression is displayed. Assignment is performed by the = operator:
invalid expression
and <istmt>: 3499 y not found
The run-time message is prefixed by an identity (<istmt> here) and a number (3499 here). Mata is telling us, “I was executing your istmt [that’s what everything you type is called] and I got error 3499, the details of which are that I was unable to find y.”
If you are reading the entries in the order suggested in [M-0] intro, see [M-1] interactive next.

数字相关英文知识点总结1. Number Systems:a. Decimal (base 10) systemb. Binary (base 2) systemc. Octal (base 8) systemd. Hexadecimal (base 16) system2. Types of Numbers:a. Natural numbersb. Whole numbersc. Integersd. Rational numberse. Irrational numbersf. Real numbersg. Complex numbers3. Operations on Numbers:a. Additionb. Subtractionc. Multiplicationd. Divisione. Exponentsf. Square roots4. Number Properties:a. Commutative propertyb. Associative propertyc. Distributive propertyd. Identity propertye. Inverse property5. Prime Numbers:a. Definition and propertiesb. Prime factorizationc. Sieve of Eratosthenes6. Divisibility:a. Divisibility tests for numbersb. Factors and multiplesc. Greatest common divisor (GCD)d. Least common multiple (LCM)7. Fractions and Decimals:a. Converting between fractions and decimalsb. Simplifying fractionsc. Operations on fractions and decimalsd. Equivalent fractions8. Percentages:a. Converting between percentages and decimals or fractionsb. Percentage changec. Percentage increase and decreased. Applications of percentages in real lifeAdvanced Concepts:1. Number Theory:a. Divisibility rulesb. Modular arithmeticc. Congruence relationsd. Fermat's little theoreme. Euler's totient function2. Irrational Numbers:a. Definitionb. Properties of irrational numbersc. Proof of the irrationality of certain numbers (e.g. square root of 2, e, pi)3. Complex Numbers:a. Definition and propertiesb. Operations on complex numbersc. Complex plane and polar formd. Applications of complex numbers in mathematics and physics4. Number Sequences and Series:a. Arithmetic sequencesb. Geometric sequencesc. Fibonacci sequenced. Convergent and divergent seriese. Summation notation5. Number Patterns:a. Pascal's triangleb. Fibonacci sequencec. Geometric patternsd. Patterns in prime numbers6. Number Systems in Computing:a. Binary and hexadecimal representationb. Fixed-point and floating-point representationc. Binary arithmeticd. Two's complement representation7. Number Systems in Cryptography:a. RSA algorithmb. Modular exponentiationc. Primality testingd. Discrete logarithm problem Applications:1. Financial Mathematics:a. Simple interest and compound interestb. Amortization schedulesc. Present value and future valued. Annuities and perpetuities2. Statistics and Probability:a. Mean, median, and modeb. Standard deviation and variancec. Probability distributionsd. Expected value and variance3. Geometry and Trigonometry:a. Pythagorean theoremb. Trigonometric functionsc. Area and volume calculationsd. Coordinate geometry4. Physics and Engineering:a. Calculus and differential equationsb. Vector mathematicsc. Fourier series and transformsd. Complex exponentials5. Computer Science:a. Data representation and bit manipulationb. Algorithms and data structuresc. Boolean algebra and logic gatesd. Cryptography and security6. Cryptography and Number Theory:a. Public key encryptionb. Digital signaturesc. Cryptographic hash functionsd. CryptanalysisConclusion:In conclusion, understanding the fundamentals of numbers and their properties is essential in various fields such as mathematics, science, engineering, finance, and technology. From basic arithmetic to advanced number theory, the applications of numbers are vast and diverse. Whether it's calculating interest on a loan, analyzing data in statistics, solving equations in physics, or encrypting data for security, numbers play a crucial role in our everyday lives. Mastering the concepts and applications of numbers can lead to a deeper understanding of the world around us and open doors to new opportunities and discoveries.。

以number的英语作文Numbers are an integral part of our daily existence, serving as the foundation for everything from counting to complex mathematical equations. They are not just symbols or abstract concepts; they are the language of science, technology, and our everyday interactions.In the realm of science, numbers are crucial. They help us measure and quantify the world around us. From the speed of light to the atomic number of elements, numbers provide the precision that scientific inquiry demands. Without them, we would not have the technological advancements that have revolutionized our lives.In mathematics, numbers are the building blocks of countless theories and proofs. They are the tools that mathematicians use to solve problems, from simple arithmetic to the most complex calculus. Numbers are infinite, and so is their potential for discovery in the field of mathematics.Economics also relies heavily on numbers. They are used to track economic indicators, such as GDP, inflation rates, and employment figures. These numerical data points are essential for making informed decisions about economic policies and strategies.On a more personal level, numbers are used to marksignificant milestones in our lives. Birth dates,anniversaries, and even social security numbers are all examples of how numbers are deeply intertwined with our identities and personal histories.Moreover, in literature and art, numbers can take on symbolic meanings, representing concepts such as unity, infinity, or balance. They can evoke emotions and convey messages beyond their literal value.In conclusion, numbers are more than just tools for calculation; they are a universal language that permeates every aspect of human endeavor. They are essential for understanding the world, for communicating ideas, and for expressing the nuances of human experience. Whether we are counting, measuring, or simply appreciating their aesthetic qualities, numbers play an indispensable role in our lives.。