fourth post will be brief. Chapter 3 was about real numbers. This chapter talks about the "magic" of complex numbers. I didn't immediately follow everything in this chapter, and don't have the time to mull it over. But the 1700s saw the realization that there were good reasons to talk about the square root of negative one.
Of course anything squared ends up positive, so there is no "real" number that multiplies by itself and turns out negative. So mathematicians of the 1700s defined a quantity "i" that multiplied by itself to equal -1.
A "complex number" is a real number plus another number times i. So these numbers have the form a + bi.
As it turns out, complex numbers are intrinsic to quantum physics. They thus do relate in a fundamental way to reality. More on that to come in future chapters.