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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 28, 2020 at 12:01am

#999252

Wait, "Dust" Can Be A Verb Too?

What with the Cyber Weekend here at WDC, I figure it's time to have another Merit Badge Mini-Contest! It's been a while. Details below.

I suppose I should answer this prompt with "beer."

PROMPT November 28th

What’s on the top of your mind right now that you need to tell someone about?

But I won't.

I'm... not the world's greatest housekeeper. I tend to put things off and they get overwhelming so I put them off some more.

Yesterday, I decided to start small: with the spice rack in the kitchen.

You know, the whole purpose of drying and keeping spices is that they don't go bad quickly, so I never paid too much attention to expiration dates on them. But as I was wiping years of accumulated dust off of some of the bottles, I noticed that they had passed their "best of" date years ago.

In my defense, I haven't been using those. Mostly, these days, I use the garlic powder, oregano, and red pepper flakes, and those were recent purchases. Had I ever had need for the tarragon, for example, well, I'd have noticed that it expired in 2015 and discarded it in favor of buying a new bottle. And it didn't look bad; it had merely lost most of its scent And yes, I noticed the scent of others, so no, my olfactory apparatus isn't compromised by the Trump Mumps. (As an aside, that particular symptom scares me more than other reported symptoms such as kidney failure, lung scarring, brain damage, or death. Not being able to smell or taste would severely cramp my style.)

The worst offender wasn't a spice at all. It was a canister of beef bouillon that had an expiration date in -- I'd be embarrassed to admit this if I were an actual human -- 2000.

Again, I haven't been using it. It's just been sitting there. Since the last millennium. Hell, I wouldn't have bought the thing in 2000 but some time before then, so it's likely the canister's old enough to legally drink.

Thing is, it's probably still viable. Probably. I wasn't about to take any chances. Into the trash went the little cubes, and into the recycling bin went the plastic bottle.

I'm hoping that this newfound interest in cleaning isn't transient, like most of my interests. The spices took over an hour to clean up and organize, and they take up maybe one cubic foot of volume in total. My house is 2000 square feet in area and 20 feet high, so... math... 39,999 cubic feet to go. In fairness, a lot of that volume is air. Dusty air... but air.

But I did also manage to take the time to deep-clean a fraction of the refrigerator, where I found a rock-solid box of baking powder that's probably been there since the first GW Bush administration, and bottles of tonic water that, if they were people, would be in middle school now. Yes, tonic water has an expiration date. Yes, I dumped the contents down the drain. I'll just have to keep drinking my gin straight.

So... 39,998 cubic feet to go.

I'm terrified of moving the refrigerator. Not even the gods know what it looks like behind there, or underneath.

Now, I don't want you to get the impression that my entire house is a mess. A good bit of clutter, sure, but the floors are clean, the food preparation areas are spotless, and I keep the bathrooms shiny. I have a cleaning service that comes in once a month to keep me honest about that sort of thing, but the only one who can do anything about the 25 years of accumulated stuff is me. I just tend to put things away and forget about them; they become fixtures. That's what I'm trying to do something about.

On the plus side, neat and organized people never make the kinds of awesome discoveries that I do. For every expired pack of baking powder, I find at least one interesting thing (not usually in the fridge though) that reminds me of something or someone from the past. This is not always a good thing, because that "someone" could be one of my ex-wives (they both lived here), but sometimes I feel like Howard Carter in Tutankhamen's tomb.

So that's what's on my mind these days. I figured I'd better write it down because maybe by doing so it'll keep me from putting it off further. The only way for me to actually get any cleaning done is to use it as a procrastination tool for something else, but I haven't figured out what the other thing is that I'm procrastinating. It has to be something that's even more distasteful to me than cleaning, but there's not much in that category. I hope it's not something important.

But also for the record, no, I'm not in the least bit interested in going minimalist. I've ranted about that shit in here before; it's mostly promoted to encourage even more consumerism.

That's no excuse for keeping expired tonic water around, though.

It's a good thing gin doesn't go bad.

Merit Badge Mini-Contest!

What's your least favorite chore? Doesn't have to be related to housecleaning as in today's entry, but it can be. Comment below. My favorite -- as defined entirely subjectively by me -- will earn the commenter a Merit Badge! As usual, you have until midnight tonight WDC time (that's the end of Saturday).

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