Imaginary Numbers Are Real [Part 7: Complex Multiplication]

This week we uncover the connection between complex multiplications and the complex plane. Our result is another approach to complex multiplication. As shown in figure 1, we know have two completely valid, but completely separate ways to multiply complex numbers. There are certainly other math problems that are solvable by various methods - but I really like this one because it reminds me that there's more to math than what we see on the page. Since these two methods look so different, but do the same exact thing, this suggests that we are only glimpsing a deeper process from different perspectives. 

Figure 1. Two ways to multiply complex numbers and the Milky Way hangin out. 

This must raise the question, what is the deeper process? What is the connection between math and our universe? Why is math unreasonably good at predicting reality? Questions like these land is firmly in the realm of metaphysics - and are questions that people have asked for thousands of years. In fact, as we saw earlier in the series, questions like these historically have slowed down the development of mathematics. 

There's no simple answer to questions like these, but they should serve to remind us that at their core, math and science are ways that we make meaning out of the world around us.

Which is pretty cool.