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.

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