复数平面

The geometric significance is the plural of students to solve plane analytic geometry and analytic geometry of space in many practical problems of the favorable tool.

复数的几何意义是学生分析、解决平面解析几何与空间解析几何中许多实际问题的有利工具。

In this thesis, we will mainly do research on the novel scheme for Digital image Steganography, Digital Image Secret Transmission in network and the development of the information hiding device for application. The main contributions of this thesis are as following: The novel conversion method for mapping image to complex number is proposed, and the plus, minus, multiply and complex conjugate operation of image are defined based on Positional number systems and complex number system. Following new results have been gotten: 1 The suitable complex number basis to be used to express integers is a big set. 2 Any image can be mapping into a one-to-one point. 3 Lots of image processing problem can be considered based on geometric theory.

在本论文中，研究工作集中在数字图像伪装算法的新模型、图像在网络中的加密传输的新方案和信息伪装设备的研发等三个方面，主要包括：基于位值制记数法和复数系理论，提出利用复数作为基底的数字图像新的表示方法，用复数运算定义了图像和图像间的"加"、"减"、"乘"、"共轭"等运算关系；得到理论结果： 1、能表示任何整数的复数基是很大的一个集合。2、任何一幅图像，都能和复平面上的一个点一一对应。3、可以将图像问题化归为平面几何问题处理。4、复数系下的图像表示适合用于信息伪装。

In Chapter 5, in geometric perspectives, the geometric properties of complex numbers are explored, including complex plane, four arithmetic operations of complex numbers and nth root of a complex number. It is also exemplified how these geometric properties are applied to solving the problems of plane geometry.

第五章从几何的观点探索复数的几何性质，包括复数平面、复数的四则运算及复数的n次方根，并举出几个例子，说明这些几何性质如何应用在解决平面几何的问题上。

In this paper,a new method is proposed to analyse the motion of plane methanism by means of complex polar coordinates vector method.

1〕本文提出用复数—极坐标矢量法来分析平面机构的运动，其优点在于分析问题时概念清晰，运算简便，且机构运动愈复杂，优越性愈明显，也为使用电子计算机编制程序提供方便。

The main contents of this course include: complex number and planar point set, function of complex variable, complex integral, series, residue, conformal mapping, analytic extension, harmonic function.

本课程的基本内容有：复数与平面点集、复变函数、复积分、级数、留数、保形映射、解析开拓、调和函数。

A concept, shadow equation, was put forward to search the real geometric meaning of complex roots for general equation.

提出了影像方程的概念，从而可以研究一般方程复数解在实平面上的几何意义。

Concerning value distribution theory, Q.C.Zhang got the following result:Let f be a non-constant meromorphic function in C, b is a finite non-zero complex number, if f and f" CM share 0 and IM share b, then: f ≡ f", or f =(2b)/(1-ce-2z) here c is any non-zero constant.

在值分布理论中，张庆彩得到了这样的结果：设f是复平面上的非常数亚纯函数，b是非零的有限复数，若f和f′CM分担o且IM分担b，则： f≡f′，或者 f=2b/1-ce-2z ，其中c是任意非零常数。

In this paper,a new algorithm is given by means of the complexification of the knots,i.e. the node in the plane is considered as a complex point,the vector as a complex vector,and then based on the construction of vector valued Thiele type rational interpolants and the backward three term recurrence relation for vector valued continued fractions,the recursive algorithm is obtained by appropriate transformation.

文章利用插值型值点复数化的方法讨论并给出了二元向量值有理插值的一种新算法，即把平面上的插值结点视为一个复数，所对应的向量视为一个复向量，使用一元Thiele型向量值有理插值公式的构造方法和向量连分式的向后三项递推关系式以及适当的变换，最后导出了这种递推算法。

At the same time, a widespread reputation has been built up in the business circle of online game development, because over 100 plane media and online media 复数?）, including such famous papers and magazines as Wenhui Daily and Shanghai Informationization, have made positive reports on "Wulong Academy".

同时，我们已经在业界取得了广泛的知名度，报道过乌龙学院的平面和网络媒体超过100家，包括《文汇报》《上海信息化》在内的上海各大报纸、杂志都对乌龙学院进行了正面报道。

This thesis makes use of complex numbers to study geometry. It mainly considers the following questions: using complex numbers to express collected points and curves on the level;geometric applications of complex numbers on collinear,concurrent,round,Mobius Mappings of Complex numbers problems,etc..Meanwhile,this thesis recommends some methods for thinking on mathematics.

本文利用复数来研究几何，主要考虑如下的问题：平面上的点集的复数表示；平面曲线的复数表示；复数在共线、共点、共圆、复数的麦比乌斯变换等几何问题上的应用，在说明这些应用的同时介绍一些数学上常用的思考方法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。