OK, so what? Well for one thing, using complex numbers allows engineers and physicists to make real world approximations using the complex plane.
Above: The complex plane
Complex numbers also connect the sinusoidal functions, sine and cosine, to the exponential function, e. The relationship between the two is critical to most modern day engineering problems. Try to puzzle through Euler's formula below.
Now for the really cool stuff. The complex plane is used to make fractals, like the ones seen below.
And finally, complex numbers can be used to puzzle your nerdy friends. What is the fourth root of 1?
i of course.