Introduction to Complex Numbers
YouTube Workbook
 Price: 129.00 kr
 Price: €13.99
 Price: £13.99
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 Price: 129.00 kr
 Price: 129.00 kr
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About the book
Description
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
Content
 What is a complex number?
 Video 1: Complex numbers are AWESOME
 Basic operations involving complex numbers
 Video 2: How to add/subtract two complex numbers
 Video 3: How to multiply a real number with a complex number
 Video 4: How to multiply complex numbers together
 Video 5: How to divide complex numbers
 Video 6: Complex numbers: Quadratic formula
 What is the complex conjugate?
 Video 7: What is the complex conjugate?
 Video 8: Calculations with the complex conjugate
 Video 9: How to show a number is purely imaginary
 Video 10: How to prove the real part of a complex number is zero
 Video 11: Complex conjuage and linear systems
 Video 12: When are the squares of z and its conjugate equal?
 Video 13: Conjugate of products is product of conjugates
 Video 14: Why complex solutions appear in conjugate pairs
 How big are complex numbers?
 Video 15: How big are complex numbers?
 Video 16: Modulus of a product is the product of moduli
 Video 17: Square roots of complex numbers
 Video 18: Quadratic equations with complex coefcients
 Video 19: Show real part of complex number is zero
 Polar trig form
 Video 20: Polar trig form of complex number
 Polar exponential form
 Video 21: Polar exponential form of a complex number
 Revision Video 22: Intro to complex numbers + basic operations
 Revision Video 23: Complex numbers and calculations
 Video 24: Powers of complex numbers via polar forms
 Powers of complex numbers
 Video 25: Powers of complex numbers
 Video 26: What is the power of a complex number?
 Video 27: Roots of comples numbers
 Video 28: Complex numbers solutions to polynomial equations
 Video 29: Complex numbers and tan (π/12)
 Video 30: Euler’s formula: A cool proof
 De Moivre’s formula
 Video 31: De Moivre’s formula: A cool proof
 Video 32: Trig identities from De Moivre’s theorem
 Video 33: Trig identities: De Moivre’s formula
 Connecting sin, cos with e
 Video 34: Trig identities and Euler’s formula
 Video 35: Trig identities from Euler’s formula
 Video 36: How to prove trig identities WITHOUT trig!
 Revision Video 37: Complex numbers + trig identities
 Regions in the complex plane
 Video 38: How to determine regions in the complex plane
 Video 39: Circular sector in the complex plane
 Video 40: Circle in the complex plane
 Video 41: How to sketch regions in the complex plane
 Complex polynomials
 Video 42: How to factor complex polynomials
 Video 43: Factorizing complex polynomials
 Video 44: Factor polynomials into linear parts
 Video 45: Complex linear factors