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 |    Not for the faint of art. |
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Complex Numbers A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number. The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi. Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary. Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty. ![Merit Badge in Quill Award
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| This week, the agent got back to me with dates for travel. I still don't have tickets in hand (or, more likely, email), so things might still change, but right now my trip's scheduled for about 9/21 to 10/10. As a bonus, she came in under my budget, even with my refusal to fly steerage. Finally, hallelujah, eureka, etc... wait. That's just four weeks away. Shit. Snuck up on me. Fortunately, there's not much else to do. I still want a travel laptop or tablet, but that's easy enough; I just have to venture (shudder) into a local retailer. Staples, maybe. Or Breast Buy. I already have a plug adapter. Maybe visit another store to buy some other clothes, but that's easy enough, too. It did occur to me that at one point, I'd heard the EU was going to start requiring visas (or visa-like applications) from US travelers, so I looked that up. {xlink:https://www.cntraveler.com/story/americans-will-need-visa-for-the-eu}Pushed back to 2025. Whew. Seems to me the travel agent would have told me if that was required, but one never knows. I think I've figured out the best way to get cash there: ATM card. Problem: I haven't used an ATM in well over a decade, so I don't actually possess a debit card. It's rare that I actually need cash, as I pay for almost everything with a credit card. The reaction to this usually surprises and disappoints me, and look, I'm hard to disappoint because I'm a pessimist. I usually get comments like "I hate credit cards" or "you must have a really low interest rate" or "wow, your debt must be crushing" or some other response about the inherent peril of using credit cards. Thing is, no, I don't pay extra. I choose cards that feature cash-back promotions, so they pay me. And funny thing about credit cards: at least for now, if you pay off the balance in full when it's due, the amount of interest charged is zero. So I basically use it like a debit card. But there's one drawback (besides needing to make an effort to stay on top of things): if you use the credit card to get a cash advance, that grace period of zero interest goes right out the window, at least for the portion of the balance that was the cash advance. I don't know exactly how it works, because I've never gotten a cash advance, but I can see that fucking up my budget for months, because it accumulates interest during the period between taking the cash advance and paying it back. Does that interest then garner further interest? I don't know, and I don't want to find out the hard way. Point is, I called my bank and asked for a debit card. I also made them give me a PIN for my primary credit card (same bank) because, apparently, some European merchants use chip-and-PIN systems instead of tap-and-signature. Ask me, that's a more secure system anyway, and I don't know why we can't adopt it here. The bank rep didn't instill a lot of confidence in me, though, because she kept saying things like "PIN number" and "automatic ATM machine." I think I reached their Department of Redundancy Department. The idea is that I expect to pay for most things in Europe with the CC, but there are some situations where cash is useful. I don't want to carry a lot of dollars, pay someone to convert them to euros, then pay someone again to convert them back to dollars as I return. At least I won't have to worry about tipping... right? Right? Back in the old days, we used traveler's cheques, but I don't think that's a thing anymore. And most of the countries I've visited up until now were cool with taking US money (though at an unfavorable exchange rate). Apparently, there's a 1% fee for using the debit card at a foreign ATM, but I think that's still cheaper (and easier) than currency exchange. Which I might still have to do on the return, but whatever. That is, unless one of you more seasoned international travelers have any better ideas. I'm open to suggestions. |
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