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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 11 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 13 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

May 13, 2022 at 12:02am

#1032338

Hypothetical

I don't know anything about this source, except that I religiously ignored its print version like I do every other magazine at the checkout counter. Or did back before I was too lazy to even shop for my own groceries. And the menu headers don't give me a lot of confidence: "Breast Cancer Starter Kit." That's... ambiguous, at best, and maybe a little horrific.

Anyway, the article.

170 Hypothetical Questions That'll Give Your Brain a Workout

I'd view the "workout" bit with skepticism, but whatever. I'm more interested in the questions. Obviously, I'm not going to paste them here. Hell, I can't be arsed to read all 170.

But of course I have comments on parts of it. Starting with the lede.

The art of conversation is changing.

Always does.

Sometimes we are so connected to our screens that we forget to “connect” with those around us.

Hey. Guess what. The people on the other end of that screen? They're people. Just like the ones around you, only better because you've selected them. Sure, you may be using the screen in solitude to play Wordle or check your stock portfolio with existential despair -- which is your prerogative -- but a lot of people use *shudder* social media, or text. They're talking to other people. They're connecting. There's nothing magical or preferred about in-person communication. In fact, people tend to sweat and fart, which you can't generally smell over the internet.

Fuck right off with your technophobic bullshit.

Once in a while, it’s nice to sit down, relax, and just talk.

Even nicer with alcohol.

But, chatting can quickly get boring when you stick to small talk.

Which is why I usually jump right in to math or science. This has the bonus effect of making most people go away.

After all, there is only so much to say about the weather.

The weather is not a safe topic of conversation. Pretty soon, someone mentions climate change, and then there's inevitably an argument.

Luckily, posing a couple of hypothetical questions can quickly turn a dull chat into an invigorating conversation.

Isn't that what Cards Against Humanity is for?

Try out these hypotheticals the next time you want to have a real conversation.

It occurs to me that Lilli 🧿 ☕

could mine this for her QOTD forum. That way, we can discuss them online, as Nature intended, rather than face-to-face.

The article, of course, goes on to list the actual questions. Some of them are silly, as expected. Others might actually have some value. A few aren't all that hypothetical.

The irony here, if you can call it that, is that if I were to use the list as intended -- in person, in meatspace, talking with another moving sack of mostly water -- there's no way I'd remember any of these questions. Nope, I'd whip out my communicator, find the website, and scroll down to the questions, thus negating the dubious benefits of being in meatspace in the first place.

But that's okay. It's not going to happen. I'm just leaving this list here for you to look at if you're interested. And if you want to address any of these questions in the comments here, go for it. I shot my wad complaining about the article's intro.

3 Like • Comment • View 5 comments

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