Real or Imaginary? Both – It’s Kind Of Complex

For most of us, real numbers are enough to do the job of day-to-day math. However, there is another set of numbers that are outside the real numbers: the unfortunately named imaginary numbers. Unfortunate, because they have real-life applications, such as in electrical engineering. Imaginary numbers are based on the square root of -1. No, you won’t go blind if you take the square root of a negative number, you just get a whole new set of numbers to play with!

Combining the set of real numbers with the set of imaginary numbers, gives us the set of complex numbers. These numbers are graphed in the complex plane, which is where fractals reside!

Newton’s Method & Fractals

I am constantly amazed at how Newton’s work can find fresh applications. Steven Strogatz has an excellent essay on complex numbers in today’s NYT, in which he goes from the  basic definition of i to how Newton’s Method for approximating roots can lead to a complex chaotic system. The video below is an illustration of this concept (Read the NYT article first, though, to understand what the video is about!):