查看“-3+2i”的源代码

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| reason          = <nowiki>内容为：'{{Vfd|过期關注度}} {{Notability|time=2010-9-19}} {{整数   | list =[[数表]] — [[複数]]   [[4i]]  [[3i]]  [[-3+2i]] [[2i]]  [[3+2i]]  [[虛數單位|i]]  [[-5]] [[-4]] [[-3]] [[-2]]  [[-1]] [[0]]  [[1]]  [[2]]  [[3]]  [[4]]  ...'</nowiki>
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{{整数
 
| list =[[数表]] — [[複数]] 

[[4i]]

[[3i]]

[[-3+2i]] [[2i]]  [[3+2i]]

[[虛數單位|i]]

[[-5]] [[-4]] [[-3]] [[-2]]  [[-1]] [[0]]  [[1]]  [[2]]  [[3]]  [[4]]  [[5]] [[6]]  [[7]]

[[-i]]

[[-3-2i]] [[-2i]]  [[3-2i]]

[[-3i]]
| 小写 = 虛數二減三
}}

'''<math>-3+2i</math>'''是位於[[複平面|複數平面]]的[[第二象限]]的[[複數_(數學)|複數]]

==数学性质==

* <math>-3+2i</math>是個[[高斯整數]]

* <math>-3+2i</math>實數部是[[-3]]虛數部是[[2]]

* <math>-3+2i</math>的[[共軛複數]]是[[-3-2i]]

* <math>-3+2i</math>也可以算是一種[[複數]]

* <math>-3+2i</math>的[[絕對值]]是<math>\sqrt{13}</math>


{{Num-stub}}

==參見==

* [[虛數]]
* [[負數]]
* [[整數]]
* [[共軛複數]]
* [[複平面|複數平面]]

==引用資料來源==
<references />
* {{Citation/core
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  |Year=1986
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  |Date = {{#if:|{{{date}}}|  1986}}{{#if:|({{{cndate}}})}}
  |Title=Functions of One Complex Variable I
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* ''An Imaginary Tale: The Story of <math>\sqrt{-1}</math>'', by Paul J. Nahin; Princeton University Press; ISBN 0-691-02795-1 (hardcover, 1998). A gentle introduction to the history of complex numbers and the beginnings of complex analysis.
* ''Numbers'', by H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch, A. Prestel, R. Remmert; Springer; ISBN 0-387-97497-0 (hardcover, 1991). An advanced perspective on the historical development of the concept of number.
* ''The Road to Reality: A Complete Guide to the Laws of the Universe'', by [[Roger Penrose]]; Alfred A. Knopf, 2005; ISBN 0-679-45443-8. Chapters 4-7 in particular deal extensively (and enthusiastically) with complex numbers.
* ''Unknown Quantity: A Real and Imaginary History of Algebra'', by John Derbyshire; Joseph Henry Press; ISBN 0-309-09657-X (hardcover 2006).  A very readable history with emphasis on solving polynomial equations and the structures of modern algebra.
* ''Visual Complex Analysis'', by [[Tristan Needham]]; Clarendon Press; ISBN 0-19-853447-7 (hardcover, 1997). History of complex numbers and complex analysis with compelling and useful visual interpretations.
* [http://www.solvemymath.com/online_math_calculator/complex_number_trigonometry/complex_number/index.php solvemymath.com Complex Numbers Calculator]
* [http://resonanceswavesandfields.blogspot.com/2007/08/eulers-equation-and-complex-numbers.html Interactive Visual Representation of Complex Numbers]
*[http://math.ntnu.edu.tw/~horng/letter/vol3no2f.htm 引用部份資料]
*[http://file.sysh.tc.edu.tw/~dick/mybookone1-4.swf 引用一點點資料]
*[http://en.wikipedia.org/wiki/Imaginary_unit#cite_ref-qcorner_0-0  ^]To find such a number, one can solve the equation <math>(x + iy)^2</math> = <math>i x^2</math> + <math>2 i x y</math> −<math> y^2</math> = <math>i</math> Because the real and imaginary parts are always separate, we regroup the terms: <math>x^2 - y^2 + 2 i x y = 0 + i</math> and get a system of two equations: <math>x^{2}-y^{2} = 0 2xy = 1</math> Substituting <math>y = \frac{1}{2} x</math> into the first equation, we get <math>x^{2}-\frac{1}{4} x^{2}</math> = <math>0 x^2 = \frac{1}{4} x^{2} 4x^{4} = 1</math> Because <math>x</math> is a real number, this equation has two real solutions for x: <math>x = 0.5^{\frac{1}{2}}</math>  and <math>x = -0.5^{\frac{1}{2}}</math> . Substituting both of these results into the equation <math>2x</math><math>y</math> = 1 in turn, we will get the same results for y. Thus, the square root of i is the number<math>0.5^{\frac{1}{2}} + i0.5^{\frac{1}{2}}</math> and <math>-0.5^{\frac{1}{2}} - i0.5^{\frac{1}{2}}</math> [http://www.math.utoronto.ca/mathnet/questionCorner/rootofi.html     University of Toronto Mathematics Network: What is the square root of i?] URL retrieved March 26, 2007.
*[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=640&bodyId=1038 Euler's work on Imaginary Roots of Polynomials] at [http://mathdl.maa.org/convergence/1/ Convergence]
*[http://www.math.utoronto.ca/mathnet/questionCorner/rootofi.html     University of Toronto Mathematics Network: What is the square root of i?]
*[http://en.wikibooks.org/wiki/High_School_Mathematics_Extensions/Supplementary/Complex_Numbers/Solutions  部分來自英文維基]
{{數學小作品}}





[[Category:複數|F]]