Why I Love this Equation

The quartic equation 16z^4 - 12z^2 + 1 = 0 has some surprising connections to geometry, trigonometry, and complex numbers. We explain these connections in depth, and conclude with how to find more equations with similar properties. 00:00 Solving 02:16 Why the solutions are interesting 04:40 Complex numbers 08:56 Complex interpretation 10:46 Geometric interpretation 12:20 Where did it come from? 12:49 Finding more equations 18:32 Odd numbers warning