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Peter Wittwer
L'équation z^2=−1 n'admet pas de solution dans R. Nous introduisons le système des nombres complexes C : C'est un corps qui contient R et qui nous permet de résoudre cette équation. Nous introduisons d'abord différentes manières de représenter un nombre complexe. Par la suite nous discutons les solutions des équations de la forme zn=w avec n∈N∗ et w∈C . Nous terminons avec un théorème plus général sur les racines de polynômes: le théorème fondamental de l'algèbre . Ce chapitre est indépendant du reste du cours; par la suite on va presque toujours considérer les nombres réels et pas les nombres complexes.
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What's inside
Learning objectives
- Définition du corps des nombres complexes
- Représentation cartésienne
- Propriétés élémentaires
- Elément inverse pour la multiplication
- Formule d'euler et de moivre
- Forme polaire d'un nombre complexe
- Résolution des équations
- Théorème fondamental de l'algèbre
- Définition du corps des nombres complexes
- Représentation cartésienne
- Propriétés élémentaires
- Elément inverse pour la multiplication
- Formule d'euler et de moivre
- Forme polaire d'un nombre complexe
- Résolution des équations
- Théorème fondamental de l'algèbre
Syllabus
Chapitre 2 : Introduction aux nombres complexes
2.1 Définition du corps des nombres complexes
2.2 Nombres complexes, représentation cartésienne
Read more
Syllabus
Chapitre 2 : Introduction aux nombres complexes
2.1 Définition du corps des nombres complexes
2.2 Nombres complexes, représentation cartésienne
Read more
2.3 Définitions additionnelles et propriétés élémentaires
2.4 Elément inverse pour la multiplication
2.5 Formule d'Euler et de Moivre
2.6 Forme polaire d'un nombre complexe
2.7 Résolution des équations
2.8 Théorème fondamental de l'algèbre
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Analyse I (partie 2) : Introduction aux nombres complexes with these
activities:
Brush Up on Real and Complex Numbers
Show steps
Reviewing the basics of real and complex numbers will strengthen your foundation for this course on complex numbers.
Browse courses on
Complex Numbers
Show steps
-
Revisit definitions of real and complex numbers.
-
Practice operations with real and complex numbers.
Explore Video Tutorials on Complex Numbers
Show steps
Watching video tutorials can provide additional clarity and reinforce your understanding of complex numbers.
Show steps
-
Search for reputable online video tutorials on complex numbers.
-
Take notes and practice the concepts presented in the tutorials.
Engage in Study Group Discussions
Show steps
Participating in study groups allows you to interact with peers, ask questions, and clarify concepts related to complex numbers.
Show steps
-
Join or form a study group with classmates.
-
Meet regularly to discuss course material, solve problems, and share insights.
Three other activities
Expand to see all activities and additional details
Show all six activities
Solve Complex Number Equations
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Practicing solving complex number equations will enhance your problem-solving skills and deepen your understanding.
Show steps
-
Find practice problems or exercises on complex number equations.
-
Attempt to solve the equations using appropriate methods.
-
Check your solutions and identify areas for improvement.
Organiser un groupe d'étude
Show steps
Former un groupe d'étude avec des pairs pour discuter des concepts, résoudre des problèmes ensemble et se soutenir mutuellement.
Browse courses on
Collaboration
Show steps
-
Trouver des pairs intéressés
-
Fixer un calendrier et un lieu de réunion réguliers
-
Préparer et animer les sessions
Présenter un exposé sur les nombres complexes
Show steps
Préparer et présenter un exposé informatif sur les nombres complexes, couvrant leurs propriétés, leurs applications et leur importance dans divers domaines.
Browse courses on
Communication
Show steps
-
Rechercher et organiser les informations
-
Créer des supports de présentation visuels et engageants
-
Pratiquer et perfectionner la présentation
Brush Up on Real and Complex Numbers
Show steps
Reviewing the basics of real and complex numbers will strengthen your foundation for this course on complex numbers.
Browse courses on
Complex Numbers
Show steps
Show steps
Show steps
- Revisit definitions of real and complex numbers.
- Practice operations with real and complex numbers.
Explore Video Tutorials on Complex Numbers
Show steps
Watching video tutorials can provide additional clarity and reinforce your understanding of complex numbers.
Show steps
Show steps
Show steps
- Search for reputable online video tutorials on complex numbers.
- Take notes and practice the concepts presented in the tutorials.
Engage in Study Group Discussions
Show steps
Participating in study groups allows you to interact with peers, ask questions, and clarify concepts related to complex numbers.
Show steps
Show steps
Show steps
- Join or form a study group with classmates.
- Meet regularly to discuss course material, solve problems, and share insights.
Three other activities
Expand to see all activities and additional details
Show all six activities
Solve Complex Number Equations
Show steps
Practicing solving complex number equations will enhance your problem-solving skills and deepen your understanding.
Show steps
Show steps
Show steps
- Find practice problems or exercises on complex number equations.
- Attempt to solve the equations using appropriate methods.
- Check your solutions and identify areas for improvement.
Organiser un groupe d'étude
Show steps
Former un groupe d'étude avec des pairs pour discuter des concepts, résoudre des problèmes ensemble et se soutenir mutuellement.
Browse courses on
Collaboration
Show steps
Show steps
Show steps
- Trouver des pairs intéressés
- Fixer un calendrier et un lieu de réunion réguliers
- Préparer et animer les sessions
Présenter un exposé sur les nombres complexes
Show steps
Préparer et présenter un exposé informatif sur les nombres complexes, couvrant leurs propriétés, leurs applications et leur importance dans divers domaines.
Browse courses on
Communication
Show steps
Show steps
Show steps
- Rechercher et organiser les informations
- Créer des supports de présentation visuels et engageants
- Pratiquer et perfectionner la présentation
Career center
Learners who complete Analyse I (partie 2) : Introduction aux nombres complexes will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists use mathematical and statistical methods to analyze data and extract insights. As a Data Scientist, you may use complex numbers to represent and analyze data. This course provides a foundation in the complex number system, which is essential for understanding the mathematical tools used in data science.
Math Teacher
Math Teacher
Math Teachers teach mathematical concepts to students at various levels. As a Math Teacher, you can help build a foundation in complex numbers for your students. This course introduces the complex number system and covers topics such as Cartesian and polar forms, which are essential for understanding higher-level mathematics concepts.
Actuary
Actuary
Actuaries use mathematical and statistical methods to assess risk and uncertainty. As an Actuary, you may use complex numbers to model financial data and make predictions. This course provides a foundation in the complex number system, which is essential for understanding the mathematical tools used in actuarial science.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and analytical skills to evaluate investments and make recommendations to clients. As a Financial Analyst, you may use complex numbers to model financial data and make predictions. This course provides a foundation in the complex number system, which is essential for understanding the mathematical tools used in financial analysis.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. As a Software Engineer, you may use complex numbers in various applications, such as computer graphics, signal processing, and numerical simulations. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in software engineering.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical methods to solve problems in business and industry. As an Operations Research Analyst, you may use complex numbers to model and analyze systems. This course provides a foundation in the complex number system, which is essential for understanding the mathematical tools used in operations research.
Electrical Engineer
Electrical Engineer
Electrical Engineers design, develop, and maintain electrical systems. As an Electrical Engineer, you may use complex numbers to analyze and design circuits and systems. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in electrical engineering.
Mechanical Engineer
Mechanical Engineer
Mechanical Engineers design, develop, and maintain mechanical systems. As a Mechanical Engineer, you may use complex numbers to analyze and design systems involving vibration, fluid flow, and heat transfer. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in mechanical engineering.
Aerospace Engineer
Aerospace Engineer
Aerospace Engineers design, develop, and maintain aircraft, spacecraft, and other aerospace systems. As an Aerospace Engineer, you may use complex numbers to analyze and design systems involving aerodynamics, propulsion, and control. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in aerospace engineering.
Chemical Engineer
Chemical Engineer
Chemical Engineers design, develop, and maintain chemical processes and systems. As a Chemical Engineer, you may use complex numbers to analyze and design systems involving chemical reactions, fluid flow, and heat transfer. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in chemical engineering.
Civil Engineer
Civil Engineer
Civil Engineers design, develop, and maintain civil infrastructure, such as roads, bridges, and buildings. As a Civil Engineer, you may use complex numbers to analyze and design structures and systems. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in civil engineering.
Biomedical Engineer
Biomedical Engineer
Biomedical Engineers design, develop, and maintain biomedical devices and systems. As a Biomedical Engineer, you may use complex numbers to analyze and design systems involving biological signals, medical imaging, and tissue engineering. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in biomedical engineering.
Nuclear Engineer
Nuclear Engineer
Nuclear Engineers design, develop, and maintain nuclear systems and components. As a Nuclear Engineer, you may use complex numbers to analyze and design systems involving nuclear reactions, radiation shielding, and heat transfer. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in nuclear engineering.
Materials Engineer
Materials Engineer
Materials Engineers develop and improve materials used in various applications. As a Materials Engineer, you may use complex numbers to analyze and design materials with specific properties, such as strength, durability, and conductivity. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in materials engineering.
Petroleum Engineer
Petroleum Engineer
Petroleum Engineers design, develop, and maintain systems for extracting and producing oil and gas. As a Petroleum Engineer, you may use complex numbers to analyze and design systems involving fluid flow, reservoir simulation, and drilling operations. This course provides a foundation in the complex number system, which is essential for understanding the mathematical concepts used in petroleum engineering.
For more career information including salaries, visit:
OpenCourser.com/course/uz7wln/analyse
Reading list
We've selected ten books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Analyse I (partie 2) : Introduction aux nombres complexes.
Un manuel complet sur les nombres complexes, avec un accent sur les applications en ingénierie et en physique.
Un texte complet sur l'analyse complexe, avec un accent sur les applications mathématiques et techniques.
Un texte avancé sur les fonctions d'une variable complexe, avec un accent sur la théorie de la fonction.
Un texte qui couvre une variété de sujets mathématiques utilisés en physique et en ingénierie, y compris les nombres complexes.
Un texte qui couvre une variété de sujets mathématiques utilisés en physique, y compris les nombres complexes.
Un texte introductif sur l'analyse complexe, avec un accent sur les applications en mathématiques et en ingénierie.
Un texte axé sur les applications des nombres complexes, avec un accent sur les techniques de calcul.
Un texte concis qui fournit une introduction aux concepts fondamentaux de l'analyse complexe.
Un guide d'étude qui fournit des problèmes résolus et des exercices de pratique sur les nombres complexes.
Un texte complet qui couvre la théorie des nombres complexes et leurs applications en mathématiques et en ingénierie.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/uz7wln/analyse
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Effort
4 to 5 hours per week for 2 weeks
Level
Introductory
Via
edX
Institution
École Polytechnique Fédérale de Lausanne
Instructor
Peter Wittwer
Language
Français
Transcript
Français
Good to know
Expands on learners' existing knowledge and educational learning to elevate their skills and understanding
Develops learners' skills and strengthens their foundation by explicitly building upon the knowledge they already have
Reinforces skills that learners may already have, strengthening their professional capabilities
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