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为何虚数为复数？而虚数如何应用于真实世界，研究虚数有甚么发现？

虚数 图片参考：baike.baidu/pic/1/11710102544318064 (1)[unreliable figure]∶虚假不实的数位 (2)[imaginary number]∶实数与虚数单位之积
亦即实部为零的复数(如3i) 在数学里，如果有某个数的平方是负数的话，那个数就是虚数了。所有的虚数都是复数。 “虚数”这个名词是17世纪著名数学家笛卡尔创制，因为当时的观念认为这是真实不存在的数位。后来发现虚数可对应平面上的纵轴，与对应平面上横轴的实数同样真实。虚数轴和实数轴构成的平面称复平面
复平面上每一点对应着一个复数。 虚数的符号 1777年瑞士数学家欧拉开始使用符号i=√(-1)表示虚数的单位。而后人将虚数和实数有机地结合起来
写成a+bi形式 (a、b为实数)，称为复数。 虚数的历史 由于虚数闯入数的领域时，人们对它的实际用处一无所知，在实际生活中似乎也没有用复数来表达的量，因此，在很长的一段时间里，人们对虚数产生过种种怀疑和误解。笛卡尔称“虚数”的本意是指他是假的；莱布尼兹在西元18世纪初则认为：“虚数是美妙而奇异的神灵隐蔽所，它几乎是既存在又不存在的两栖物。”欧拉尽管在许多地方用了虚数，但又说一切形如√(-1)、√(-2)的数学式都是不可能有的，纯属虚幻的。 欧拉之后，挪威的一个测量学家维塞尔，提出把复数a+bi用平面上的点（a，b）来表示。后来，高斯提出了复平面的概念，终于使复数有了立足之地，也为复数的应用开辟了道路。现在，复数一般用来表示向量（有方向的数量)
这在力学、地图学、航空学中的应用是十分广泛的。虚数越来越显示出其丰富的内容，真是：虚数不虚。 不表示实在数量的数词。如下面例子中的一、三、五、九、百、千、万等数词都是虚数。【例】以一当十｜三五成群｜千方百计｜万紫千红｜九牛一毛｜龙生九子｜三月不知肉味｜。 描述虚数 虚数 原作：劳伦斯·马克·莱瑟（阿姆斯壮大西洋州立学院） 翻译：徐国强 虚文自古向空构，艾字如今可倍乘。 所问逢人惊诧甚，生活何处有真能？ 嗟哉小试调音放，讶矣大为掌夜灯。 三极管中知用否，交流电路肯咸恒。 凭君漫问荒唐义，负值求根疑窦增。 情类当初听惯耳，事关负数见折肱。 几分繁复融学域，百计联席悦有朋。 但看几何三角地，蓬勃艾草意同承。 Imaginary number 图片参考：upload.wikimedia/ *** /mons/thumb/5/52/Gaussebene_Koordinatendarstellung/180px-Gaussebene_Koordinatendarstellung 图片参考：en. *** /skins-1.5/mon/images/magnify-clip In mathematics
an imaginary number (or purely imaginary number) is a plex number whose square is a negative real number. Imaginary numbers were defined in 1572 by Rafael Bombelli. At the time
such numbers were thought not to exist
much as zero and the negative numbers were regarded by some as fictitious or useless. Many other mathematici were slow to believe in imaginary numbers at first
including Descartes who wrote about them in his La Géométrie
where the term was meant to be derogatory.[1] Contents 1 Definition 1.1 Corollary 2 Geometric interpretation 3 Applications of imaginary numbers 4 History 5 See also 6 References 7 External links Definition Any plex number
z
can be written as 图片参考：upload.wikimedia/math/e/7/7/e77e0e682bd347e9e7e1dec878ce8586
where 图片参考：upload.wikimedia/math/6/0/7/607708482f5a2afc26174c21834baad3 is the imaginary unit
which has the defined property that: 图片参考：upload.wikimedia/math/4/4/b/44b33da6be905320353c4c1906ac7d29 The number 图片参考：upload.wikimedia/math/b/1/9/b19dfd822e2517400335d53c1556df72
defined by 图片参考：upload.wikimedia/math/4/e/0/4e0de3698dfd4a9ab0032ace23583f6f is the real part of the plex number
图片参考：upload.wikimedia/math/e/d/f/edffd1a73cb003cdba3d07600e9aa8f2
defined by 图片参考：upload.wikimedia/math/3/2/f/32fa1bd11a7cdfce10d45ef678d142a8 is the imaginary part. Although Descartes originally used the term "imaginary number" to mean what is currently meant by the term "plex number"
the term "imaginary number" today usually me a plex number with a real part equal to 0
that is
a number of the form i y. Zero (0) is the only number that is both real and imaginary. Corollary 图片参考：upload.wikimedia/math/b/0/0/b002b9e332482fd34f834c5b113e6493 图片参考：upload.wikimedia/math/8/3/4/834b498313a7d9d60031a206f2be9222 图片参考：upload.wikimedia/math/1/3/e/13e54d9243a424ab9ded92569cefda7c … and so on. Geometric interpretation Geometrically
imaginary numbers are found on the vertical axis of the plex number plane
allowing them to be presented orthogonal to the real axis. One way of viewing imaginary numbers is to consider a standard number line
positively increasing in magnitude to the right
and negatively increasing in magnitude to the left. At 0 on this x-axis
draw a y-axis with "positive" direction going up; "positive" imaginary numbers then "increase" in magnitude upwards
and "negative" imaginary numbers "decrease" in magnitude downwards. This vertical axis is often called the "imaginary axis" and is denoted 图片参考：upload.wikimedia/math/f/9/d/f9d3b767e53c2f6939003eef8c0690ed or simply Im. In this model
multiplication by − 1 corresponds to a rotation of 180 degrees about the origin. Multiplication by i corresponds to a 90-degree rotation in the "positive" direction (i.e. counter-clockwise)
and the equation i2 = − 1 is interpreted as saying that if we apply 2 90-degree rotations about the origin
the result is a single 180-degree rotation. Note that a 90-degree rotation in the "negative" direction (i.e. clockwise) also satisfies this interpretation. This reflects the fact that − i also solves the equation x2 = − 1 — see imaginary unit. In electrical engineering and related fields
the imaginary unit is often written as j to avoid confusion with a changing current
traditionally denoted by i. Applications of imaginary numbers ...
参考: Wikipedia
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