Introduction to Complex Numbers

YouTube Workbook
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76 pages
Langue:
 English
This ebook makes learning "complex" numbers easy through an interactive, fun and personalized approach. Features include: live YouTube video streams and closed captions that translate to 90 languages!
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A propos de l'auteur

“With more than a million YouTube hits, Dr Chris Tisdell is the equivalent of a best-selling author or chart-topping musician. And the unlikely subject of this mass popularity? University mathematics.” [Sydney Morning Herald, 14/6/2012 http://ow.ly/o7gti].

Chri...

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This ebook makes learning "complex" numbers easy through an interactive, fun and personalized approach. Features include: live YouTube video streams and closed captions that translate to 90 languages!

Complex numbers "break all the rules" of traditional mathematics by allowing us to take a square root of a negative number. This "radical" approach has fundamentally changed the capabilities of science and engineering to enhance our world through such applications as: signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. A particularly beautiful connection between art and complex numbers lies in fractals, such as the Mandelbrot set.

Download this ebook and subscribe to the author's YouTube channel for more! http://www.YouTube.com/DrChrisTisdell

  1. What is a complex number?
    1. Video 1: Complex numbers are AWESOME
  2. Basic operations involving complex numbers
    1. Video 2: How to add/subtract two complex numbers
    2. Video 3: How to multiply a real number with a complex number
    3. Video 4: How to multiply complex numbers together
    4. Video 5: How to divide complex numbers
    5. Video 6: Complex numbers: Quadratic formula
  3. What is the complex conjugate?
    1. Video 7: What is the complex conjugate?
    2. Video 8: Calculations with the complex conjugate
    3. Video 9: How to show a number is purely imaginary
    4. Video 10: How to prove the real part of a complex number is zero
    5. Video 11: Complex conjuage and linear systems
    6. Video 12: When are the squares of z and its conjugate equal?
    7. Video 13: Conjugate of products is product of conjugates
    8. Video 14: Why complex solutions appear in conjugate pairs
  4. How big are complex numbers?
    1. Video 15: How big are complex numbers?
    2. Video 16: Modulus of a product is the product of moduli
    3. Video 17: Square roots of complex numbers
    4. Video 18: Quadratic equations with complex coefcients
    5. Video 19: Show real part of complex number is zero
  5. Polar trig form
    1. Video 20: Polar trig form of complex number
  6. Polar exponential form
    1. Video 21: Polar exponential form of a complex number
    2. Revision Video 22: Intro to complex numbers + basic operations
    3. Revision Video 23: Complex numbers and calculations
    4. Video 24: Powers of complex numbers via polar forms
  7. Powers of complex numbers
    1. Video 25: Powers of complex numbers
    2. Video 26: What is the power of a complex number?
    3. Video 27: Roots of comples numbers
    4. Video 28: Complex numbers solutions to polynomial equations
    5. Video 29: Complex numbers and tan (π/12)
    6. Video 30: Euler’s formula: A cool proof
  8. De Moivre’s formula
    1. Video 31: De Moivre’s formula: A cool proof
    2. Video 32: Trig identities from De Moivre’s theorem
    3. Video 33: Trig identities: De Moivre’s formula
  9. Connecting sin, cos with e
    1. Video 34: Trig identities and Euler’s formula
    2. Video 35: Trig identities from Euler’s formula
    3. Video 36: How to prove trig identities WITHOUT trig!
    4. Revision Video 37: Complex numbers + trig identities
  10. Regions in the complex plane
    1. Video 38: How to determine regions in the complex plane
    2. Video 39: Circular sector in the complex plane
    3. Video 40: Circle in the complex plane
    4. Video 41: How to sketch regions in the complex plane
  11. Complex polynomials
    1. Video 42: How to factor complex polynomials
    2. Video 43: Factorizing complex polynomials
    3. Video 44: Factor polynomials into linear parts
    4. Video 45: Complex linear factors
Muy bueno
9 octobre 2018 à 21:35
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