An introduction to adding, subtracting and multiplying complex numbers. [Algebra: Lesson 34 of 86]
- Author:
- Khan, Salman
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A demonstration of calculating i, raised to arbitrarily high exponents. [Algebra: Lesson 32 of 86]
- Author:
- Khan, Salman
A demonstration of calculating i, raised to arbitrarily high exponents.
- Author:
- Khan, Salman
An introduction to adding, subtracting and multiplying complex numbers.
- Author:
- Khan, Salman
A demonstration of dividing complex numbers and complex conjugates.
- Author:
- Khan, Salman
A demonstration of dividing complex numbers and complex conjugates. [Algebra: Lesson 35 of 86]
- Author:
- Khan, Salman
This 10-minute video lesson looks at imaginary and complex numbers.
- Author:
- Khan, Salman
This 10-minute video lesson looks at imaginary and complex numbers.
- Author:
- Khan, Salman
An introduction to i and imaginary numbers.
- Author:
- Khan, Salman
An introduction to i and imaginary numbers. [Algebra: Lesson 31 of 8]
- Author:
- Khan, Salman
An explanation of i as the principal square root of -l.
- Author:
- Khan, Salman
An explanation of i as the principal square root of -l. [Algebra: Lesson 33 of 86]
- Author:
- Khan, Salman
This 7-minute video lesson continues to look at number sets.
- Author:
- Khan, Salman
This 3-minute video lesson continues to look at number sets.
- Author:
- Khan, Salman
Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.
- Author:
- Herbert Gross
This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable. Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable. Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear. Upon successful completion of this course, the student will be able to: manipulate complex numbers in various representations, define fundamental topological concepts in the context of the complex plane, and define and calculate limits and derivatives of functions of a complex variable; represent analytic functions as power series on their domains and verify that they are well-defined; define a branch of the complex logarithm; classify singularities and find Laurent series for meromorphic functions; state and prove fundamental results, including CauchyĺÎĺ_ĺĚĺ_s Theorem and CauchyĺÎĺ_ĺĚĺ_s Integral Formula, the Fundamental Theorem of Algebra, MoreraĺÎĺ_ĺĚĺ_s Theorem and LiouvilleĺÎĺ_ĺĚĺ_s Theorem; use them to prove related results; calculate contour integrals; calculate definite integrals on the real line using the Residue Theorem; define linear fractional transformations and prove their essential characteristics; find the image of a region under a conformal mapping; state, prove, and use the Open Mapping Theorem. This free course may be completed online at any time. (Mathematics 243)
This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.
- Author:
- Illustrative Mathematics
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.
- Author:
- The Open University
This 2-minute video lesson introduces Khan's series on complex numbers.
- Author:
- Khan, Salman
This single minute video lesson looks at how to add complex numbers.
- Author:
- Khan, Salman