Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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Writer_Mike

about 9 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

March 31, 2023 at 10:45am

#1047230

Being a Pill

Very close to completing all the prompts at "JAFBG"

[XGC]...

Tell us about something/someone that fucked you off this week.

Ah, yes, the recurring reason to rant. Thing is, if I'd drawn this prompt with my random numbers earlier this month, I would have been stumped. For most of it, I didn't experience more than minor inconvenience, nothing worthy of a full-blown rant.

All that changed starting last Saturday.

Friday, with two pills left in each of my daily prescriptions, I called the pharmacy for refills. This is an automated system, which is fine; you just key in the prescription number for each one, the robot confirms it, and then, when you're done, you get told when they'll be ready for pickup. In this case, they clearly and unambiguously said "Saturday at 11 am."

Now, there's something else you need to know about my prescriptions. I think I've ranted about it before, but just to recap: My insurance sucks. The doctor sends a prescription for a 90-day supply. If I use my insurance, I have to get a 30-day supply, and it costs about $30. Here's the whatthe part: If I don't use insurance for the prescription, they happily sell me a 90-day supply. For about $30.

You read that right: With insurance, $90 for a 90-day supply. Without insurance, $30 for a 90-day supply.

There are other details, but that's the outline of it. So, getting back to the timeline here, remember, the prescriptions would be ready by 11am on Saturday. Well, I had other stuff to do Saturday, so I showed up at the pharmacy at 3pm. This particular pharmacy is in a grocery store, and I'm pretty sure they have standing orders to delay things to encourage people to shop. Still, I fully expected that, having been told the pills would be ready at 11, surely, definitely, without fail, they'd be done four hours later?

If you're reading this, you can guess what didn't happen.

And this wasn't the usual "oh, it'll be ready in 20 minutes; why don't you take a look at our lovely endcap displays and seasonal merchandise while you wait." No, it was "It might take an hour or so, if you want to come back." Well, I told them I'd come back the next day. Which was, if you've been keeping track, Sunday.

I walk in and the cashier is like "I can't find it."

I felt rage boiling up inside me. None of those pills are specifically for rage, either pro or con, but I'd cut it too close: failure to receive my prescriptions that day would mean missing at least one dose. Which, to be fair, probably wouldn't kill me, but I'd feel obligated to report it to my doctor later, and she'd undoubtedly shake her head in disapproval. Which is crushing.

So it wasn't really about the pills themselves, at this point. It was more about being jerked around by robots and cashiers. "But Waltz, isn't that just another minor inconvenience?" Yes, except that I have to deal with some kind of bullshit every time I get the pills, which, if you're following along, you know is four times a year. It wears on me. At least it's not 12 times a year, though, right?

My boil was short-lived, however; she somehow found the prescriptions. But then my brain went to: "Okay, if they forgot and used insurance, I'm going to blow my shit."

Fortunately, everything was in order. So the saga ends, anticlimactically, but at least without bloodshed.

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