These quizzes explore complex numbers: from the basics of the arithmetic up to some surprising applications such as the making of Mandelbrot's famous fractal.

By the end of these quizzes, and throughout this exploration, you'll see that complex numbers are practical, sensible, and beautiful, not just a weird and difficult-to-understand mathematical curiosity.

We'll start with the arithmetic of complex numbers, so problems like these can be tackled with ease: \[ i + i^2 + i^3 + \cdots + i^{40} = \ ? \]

By the end of these quizzes, you'll understand how to use complex numbers to generate fractals like this one: