‘Numbers but not as we know them’ introduces complex numbers. The construction of complex numbers is simpler than that of real numbers. We can say that real numbers are all possible decimal expansions, but how do we add together two infinitely non-recurring decimals? The imaginary unit allows for the construction of complex numbers, which are most easily shown graphically in the complex plane. Arithmetic can be performed on complex numbers, and they have applications in many settings, for example in trigonometry. Complex numbers can also be multiplied using matrices. Beyond the complex plane lie the groups of numbers known as quaternions and octions.