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1、第三章 数系的扩充与复数的引入3.1.1 数系的扩充和复数 的概念Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.问题提出1.数的概念产生和发展的历史进程： 正分数正无理数零和负数NQRR
2、数系每次扩充的基本原则： 第一、增加新元素； 第二、原有的运算性质仍然成立； 第三、新数系能解决旧数系中的矛盾.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.2.若 ，则对此你有什么困惑
3、？问题提出Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.3.唯物辨证法认为，事物是发展变化的，事物内部的矛盾运动是推动事物向前发 展的根本动力.由于实数的局限性，导致 某些数学问题出现矛
4、盾的结果，数学家 们预测，在实数范围外还有一类新数存在，还有比实数集更大的数系.问题提出Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation
5、 only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.1、由 得 ，这与 矛盾的原因是什么？方程x2x10无实根 2、方程x2x10无实根的根本原 因是什么？ 1不能开平方 问题探究Evaluation only.Evaluation only.
6、 Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.3、我们设想引入一个新数，用字母i表 示，使这个数是1的平方根，即 i2 1，那么方程x2x10的根是什 么？问题提出Evaluation only.Evaluation only. Created wi
7、th Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.4、若x41，利用i21,则x等于 什么？1，1，i，i. 问题提出Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client
8、 Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.5、满足i21的新数i显然不是实数， 称为虚数单位，根据数系的扩充原则， 应规定虚数单位i和实数之间的运算满 足哪些运算律？乘法和加法都满足交换律、结合律， 乘法对加法满足分配律.问题探究Evaluation only.Evaluation only. Created with Aspose.Sl
9、ides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.6、设aR，下列运算正确吗？问题探究Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created wit
10、h Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.1、虚数单位i与实数进行四则运算， 可以形成哪种一般形式的数？ abi（a，bR）2、把形如abi（a，bR）的数叫做 复数，全体复数所成的集合叫做复数集 ，记作C，那么复数集如何用描述法表 示？Cabi|a，bR问题探究Evaluation only.Evaluation only. Created with Aspose.Slides for .N
11、ET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.3、复数通常用字母z表示，即 zabi（a，bR），这一表示形式 叫做复数的代数形式，其中a与b分别 叫做复数z的实部与虚部，那么复数 z 3i的实部和虚部分别是什么？实部为 ,虚部为3.问题探究Evaluation only.Evaluation only. Creat
12、ed with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.4、两个实数可以相等，两个复数也 可以相等，并且规定：abicdi （a，b，c，dR）的充要条件是ac 且bd，那么abi0的充要条件是 什么？ab0问题探究Evaluation only.Evaluation o
13、nly. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.5、对于复数zabi（a，bR） 当b0时，z为什么数？由此说明实 数集与复数集的关系如何？当b0时z为实数. 实数集R是复数集C的真子集. 问题探究Evaluation only.Evaluat
14、ion only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.6、对于复数zabi（a，bR）当 b0时，z叫做虚数，当a0且b0时 ，z叫做纯虚数，那么虚数集与纯虚数 集之间如何？纯虚数集是虚数集的真子集. 问题探究Evaluation only
15、.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.7、复数集、实数集、虚数集、纯虚 数集之间的关系用韦恩图怎样表示 ？ 复数实数 虚数纯虚数问题探究8、两个实数可以比较大小，一个实数与 一个虚数或两个虚数可以比较大小吗？
16、虚数不能比较大小.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例1 实数m取什么值时，复数 zm1(m1)i分别是实数 ，虚数和纯虚数？ 当m1时，z是纯虚数. 典例讲评当m1时，z是实数；当m1时，z是虚数；Evaluation only.Evaluation onl
