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::::You know, it's extremely difficult to respond to an 8.5K post. My original response was a little over 2K, and I was feeling like it was already way too long. So, I'm going to focus on what seems to be your main complaint here{{snd}}that we should immediately define complex numbers as ordered pairs along with the operations thereon.
::::{{pb}}This is a non-starter. Writing {{math|(''a'', ''b'')}} is only superficially different from writing {{math|''a'' + ''bi''}}, and not having the {{mvar|i}} present makes the multiplication formula, in particular, much more opaque. It's the exact same definition, but with different notation. Just as (if not more) important is that it's notation that's just not really used in practice, either in introductory material, or even in a modern complex analysis text. If you're so focused on a modern definition, the obvious choice is as <math>\mathbb{R}[x]/(x^2 + 1).</math> This can be {{em|briefly}} mentioned early on, but anything more than that is too technical and should be reserved for later in the article.
::::This is a pretty fundamental article, and we should be making it as accessible as possible. This means we shouldn't be expecting someone reading it to be a university student. A good place to aim here is probably someone with at most a reasonable grasp of high school algebra (at least for the beginning of the article; it's okay to get more advanced as we go). We also have to be very careful because education terminology is different around the world, as is when concepts are generally introduced. I, for example, first saw complex numbers in high school algebra, well before I got to college. Maybe that's different elsewhere, but as an encyclopedia, we're really
== Worst math article ever ==
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