• Title/Summary/Keyword: Complex Number

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The algebraic completion of the rational numbers based on ATD (ATD에 근거한 유리수의 대수학적 completion에 관한 연구)

  • Kim, Boo-Yoon;Chung, Gyeong-Mee
    • The Mathematical Education
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    • v.50 no.2
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    • pp.135-148
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    • 2011
  • We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

On Teaching Materials by Using the Rotations about the Origin and the Reflections in Lines through the Origin

  • Tanaka Masaki;Yamaguti Kiyosi
    • Research in Mathematical Education
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    • v.9 no.3 s.23
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    • pp.257-267
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    • 2005
  • When notions of numbers are expanded from natural number to complex number, a similar mathematical phenomenon can be observed in each number. As a case study, to complex number, the phenomenon is investigated carefully and teaching materials are created. Then complex number is expressed with matrices and is geometrically treated, so a new number which is an extension of complex number is discovered. Thus, teaching material regarding to complex number and matrices is made for students of ordinary level. Moreover, for talented students, material about an extension of complex number can be added to the previous one.

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Evolution of Geometric Interpretation of Complex Number : Focused on Descarte, Wallis, Wessel (복소수의 기하적 해석의 발달 : Descarte, Wallis, Wessel를 중심으로)

  • Lee, Dong-Hwan
    • Journal for History of Mathematics
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    • v.20 no.3
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    • pp.59-72
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    • 2007
  • In this paper we find the germ of geometric interpretation of complex number in the Euclid Element and try to show the evolution of geometric interpretation of complex number by through Descarte, Wallis, Vessel. As a result, relations and differences between them are found. They related line with complex number and interpreted complex number geometrically by generalizing the multiplication operation.

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Complex number on textbooks and Analysis on understanding state of students (교과서에 표현된 복소수와 이에 대한 학생들의 이해 실태 분석)

  • Park, Seon-Ho;Pyo, Sung-Soo
    • The Mathematical Education
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    • v.51 no.1
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    • pp.1-19
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    • 2012
  • In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.

The correlation between learners' psychological and social factors and syntactic complexity of L2 Korean speaking (한국어 학습자의 심리적, 사회적 요인과 구어 통사 복합도 간의 상관관계)

  • Kim, Youngjoo;Baik, Juno;Lee, Sunjin;Oh, Jinhee;Jung, Hyewon
    • Journal of Korean language education
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    • v.28 no.2
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    • pp.1-36
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    • 2017
  • This study investigated the correlation between learners' psychological and social factors and their syntactic complexity of speaking. The study collected samples of Korean spoken production of 61 learners with English, Chinese, Japanese and other L1 backgrounds and applied mini-TOPIK, mini-AMTB, and SASIQ for 70 minutes. The study found that: (i) integrative motivation showed positive correlation with a number of simple complex clauses, but instrumental motivation correlated negatively with a number of adverbial clauses, indicating that high motivation hindered producing highly complex clauses although it triggered producing simple complex clauses, (ii) social contact with L2 native speakers showed positive correlation with general L2 development and a number of simple complex clauses, but revealed negative correlation with double or triple complex clauses, (iii) hours of L2 listening showed very strong positive correlation with producing triple complex clauses and general proficiency, but indicated negative correlation with a number of simple complex clauses. The study reported that high motivation toward Korean learning and active social activities with Korean native speakers helped produce simple complex clauses while hours of listening to Korean helped produce triple complex clauses.

Optimal Sampling Plans of Reliability Using the Complex Number Function in the Complex System

  • Oh, Chung Hwan;Lee, Jong Chul;Cho, Nam Ho
    • Journal of Korean Society for Quality Management
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    • v.20 no.1
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    • pp.158-167
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    • 1992
  • This paper represents the new techniques for optimal sampling plans of reliability applying the mathematical complex number(real and imaginary number) in the complex system of reliability. The research formulation represent a mathematical model Which preserves all essential aspects of the main and auxiliary factors of the research objectives. It is important to formule the problem in good agreement with the objective of the research considering the main and auxilary factors which affect the system performance. This model was repeatedly tested to determine the required statistical chatacteristics which in themselves determine the actual and standard distributions. The evaluation programs and techniques are developed for establishing criteria for sampling plans of reliability effectiveness, and the evaluation of system performance was based on the complex stochastic process(derived by the Runge-Kutta method. by kolmogorv's criterion and the transform of a solution to a Sturon-Liouville equation.) The special structure of this mathematical model is exploited to develop the optimal sampling plans of reliability in the complex system.

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Analysis of planar optical waveguides using incident angle of complex number (복소수 입사각을 이용한 평판 광도파로 해석)

  • 임영준;김창민
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.33A no.5
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    • pp.149-154
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    • 1996
  • We propose the concept of incident angle of complex number and analyze planar optical waveguides by applying the concept. The incident angle of complex number is concerned with the modeling of prism-gap-waveguide structures. It is shown that, when optical waveguides are analyzed by use of the transfer matrix method, the proposed concept enable us to find solutions faster and more accurately than ghatak's method which introduces the leaky structure.

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A Study on the Proper Equipments and Optimal Dimension for a Fitness Facility in an Apartment Complex According to the Number of Users - Focused on the four Apartments located in Cheonan - (아파트 단지 내 휘트니스 시설의 이용자수에 따른 적정 시설과 공간규모에 관한 연구 - 천안시 4개 아파트 단지를 대상으로 -)

  • Park, Young-Sun;Ryu, Soo-Hoon
    • Journal of the Korean housing association
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    • v.19 no.6
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    • pp.1-8
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    • 2008
  • A fitness facility in an apartment complex is not a simple sports facility. It has important roles in improving the residents' physical and mental health, and in forming a sense of community. This study analyzed the number of users in the fitness facility of the apartment complex, which is a significant criterion in determining the dimension. A comparative analysis between the past and the present function and dimension was performed in finding out the optimal solutions. In conclusion, the number of users in the fitness facility is influenced not by the number of households in the complex but by the facility's size and creating a desired environment. The users' favorite sports equipments were figured out to meet those needs. Moreover, comparing the facilities' size, user satisfaction, area per person, an optimal dimension for the facility, and rates of equipments were found out.

The Morphologic Study of the Mitral Valve Complex in Korean Adult Hearts (한국 성인 심장의 승모판 복합체에 관한 형태학적 연구)

  • O, Jung-Hwan;Lee, Gyu-Seok;Park, Hyeong-U
    • Journal of Chest Surgery
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    • v.23 no.6
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    • pp.1128-1138
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    • 1990
  • The mitral valve is not a simple but a complex structure, mitral valve complex. This complex is composed of mitral orifice, annulus, valve leaflet, chordae tendineae and papillary muscles. There were many controversies about this structures. We studied mitral valve complex in 63 cases of normal Korean adults, such as the circumference of mitral annulus, the intercommissural diameter, height and breadth of the cusps, including commissure, the ratio of rough to clear zone, breadth of the achordal zone, the number of scallops of posterior cusp, the number, length and the pattern of arrangement of the several types of chordae, the number and morphological characteristics of papillary muscles.

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Improvement of image processing speed of the 2D Fast Complex Hadamard Transform

  • Fujita, Yasuhito;Tanaka, Ken-Ichi
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 2009.01a
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    • pp.498-503
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    • 2009
  • As for Hadamard Transform, because the calculation time of this transform is slower than Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT), the effectiveness and the practicality are insufficient. Then, the computational complexity can be decreased by using the butterfly operation as well as FFT. We composed calculation time of FFT with that of Fast Complex Hadamard Transform by constructing the algorithm of Fast Complex Hadamard Transform. They are indirect conversions using program of complex number calculation, and immediate calculations. We compared calculation time of them with that of FFT. As a result, the reducing the calculation time of the Complex Hadamard Transform is achieved. As for the computational complexity and calculation time, the result that quadrinomial Fast Complex Hadamard Transform that don't use program of complex number calculation decrease more than FFT was obtained.

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