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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“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].

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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

- 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