• 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.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.4
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• pp.182-188
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• 2013

In this paper, we propose a complex-valued support vector machine (SVM) classifier which process the complex valued signal measured by pulse doppler radar (PDR) to identify moving targets from the background. SVM is widely applied in the field of pattern recognition, but features which used to classify are almost real valued data. Proposed complex-valued SVM can classify the moving target using real valued data, imaginary valued data, and cross-information data. To design complex-valued SVM, we consider slack variables of real and complex axis, and use the KKT (Karush-Kuhn-Tucker) conditions for complex data. Also we apply radial basis function (RBF) as a kernel function which use a distance of complex values. To evaluate the performance of the complex-valued SVM, complex valued data from PDR were classified using real-valued SVM and complex-valued SVM. The proposed complex-valued SVM classification was improved compared to real-valued SVM for dog and human, respectively 8%, 10%, have been improved.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.10B
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• pp.1482-1490
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• 2001

디지털 통신 시스템 및 신호처리 회로의 핵심 연산블록으로 사용될 수 있는 복소수 승산기 코어의 파라미터화된 소프트 IP (Intellectual Property)를 설계하였다. 승산기는 응용분야에 따라 요구되는 비트 수가 매우 다양하므로, 승산기 코어 IP는 비트 수를 파라미터화하여 설계하는 것이 필요하다. 본 논문에서는 복소수 승산기의 비트 수를 파라미터화 함으로써 사용자의 필요에 따라 승수와 피승수를 8-b∼24-b 범위에서 2-b 단위로 선택하여 사용할 수 있도록 하였으며, GUI 환경의 코어 생성기 PCMUL_GEN는 지정된 비트 크기를 갖는 복소수 승산기의 VHDL 모델을 생성한다. 복소수 승산기 코어 IP는 redundant binary (RB) 수치계와 본 논문에서 제안하는 새로운 radix-4 Booth 인코딩/디코딩 회로를 적용하여 설계되었으며, 이를 통해 기존의 방식보다 단순화된 내부 구조와 고속/저전력 특성을 갖는다. 설계된 IP는 Xilinx FPGA로 구현하여 기능을 검증하였다.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.141-152
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• 2008

In this article, the didactical analysis of complex numbers was explored in the context of mathematical connection. The result of the analysis can provide the useful tools for problem solving. The article shows that the complex numbers system plays the key roles in the school mathematics.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.69-82
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• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.53-75
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• 2012

When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

• School Mathematics
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• v.10 no.3
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• pp.357-374
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• 2008

The complex number system is supposed to introduce first chapter in the first grade of high school. When number system is expanded to complex numbers, the main aim is to understand preservation of algebraic structure with regard to the flow of curriculum and textbook. This research reviewed overall alternative articulation and treatment of textbooks from a logical viewpoint. Two research questions are developed below. First, in the structure of the current curriculum, when we consider student's 'level', how are the alternative articulation and treatment of textbooks in complex unit on a logical point of view? Second, What are more logical alternative articulation and treatment? What alternative articulation and treatment are suitable for a running goal? and what are the improvement which is definitive?

• Proceedings of the KIEE Conference
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• 2007.10a
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• pp.59-60
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• 2007

본 논문에서는 선형 비최소위상(NMP, Nonminimum Phase) 시스템에서 특정 조건을 만족하는 복소수 NMP 영점을 가진 시스템에서 언더슈트가 발생함을 보이고자 한다. 먼저 중복 실수 NMP 영점을 갖는 시스템에서의 언더슈트의 크기를 추정한다. 이를 바탕으로 복소수 NMP 영점을 가진 시스템을 중복 실수 NMP 영점을 갖는 시스템과 나머지 시스템의 합으로 보고 언더슈트가 발생하는 복소수 NMP 영점의 범위를 구한다. 최종적으로 복소수 NMP 영점의 복소수 항이 특정 제시되는 값보다 작을 때 언더슈트가 발생함을 보인다.

• Proceedings of the KIPE Conference
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• 2004.11a
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• pp.10-13
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• 2004

본 논문에서는 복소수 벡터 기법으로 설계된 동기 좌표계 비례 적분(PI) 전류 제어기의 새로운 안티 와인드업(anti-windup) 기법을 제안한다. 복소수 벡터로 설계된 동기 좌표계 비례 적분 전류 제어기는 시스템 파라메터(parameter) 변동에 더 강인하다고 알려져 있다. 그러나 이 제어기의 안티 와인드업에 대한 연구는 아직 잘 이루어지지 않았다. 제어기는 그 구조에 따라 알맞은 안티 와인드업이 필요하게 되고, 적절치 못한 안티 와인드업 기법은 제어 시스템의 동특성을 저하시킬 수 있다. 그래서 복소수 벡터로 설계된 동기 좌표계 비례 적분 전류 제어기에 알맞은 안티 와인드업 기법을 제안하였고, 제안된 알고리즘(algorithm)의 유효성은 실험을 통하여 검증하였다.