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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.
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