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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 23 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

a day 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.

December 14, 2019 at 1:17am

#971433

Unwritten, Expanded

I'm back! Actually been back a while, but it's taken me this long to recover enough from my trip to concentrate on a blog entry. This getting-old shit sucks.

Today's link is from several months ago, but I think the underlying information is worth highlighting, if only to mock the living hell out of it. I touched on some of this in this week's Comedy newsletter, "Unwritten"

, but I can get more personal (and snarky) here.

https://www.usatoday.com/story/tech/2019/02/22/15-unwritten-rules-calling-textin...

'Use at least one Emoji per text': The new rules of communicating in the digital era

And already my bullshit meter needs replacement, because the headline broke it. I, and the people I text with regularly (a select few), use emojis sparingly, if at all. We also use complete words, spelled correctly (absent the inevitable occasional typo), and proper punctuation.

Yeah, it takes longer, but it's less annoying.

But also easier is unwittingly getting caught up in a major disconnect by violating a tangle of new rules for communicating. A big one for some: Don't call until you've texted to confirm it's OK to call. But that's just the beginning.

As I pointed out in the newsletter, once you've done an article like the one I'm linking here, the rules are no longer "unwritten." By definition. However, they're not necessarily "rules," either. This one, for example? Whatever. If someone has my phone number, I expect they might call at some point. That's okay. As long as they don't expect me to answer, especially if they're not on my contact list. Any unidentified number is a health insurance telemarketer, as far as I'm concerned.

Come to think of it, I wasn't plagued by insurance scam calls all week. Could this be because I finally signed up for an Obamacare plan? Yes, I'm going to have health insurance, after two years without any. Thing is, how the fuck do the telemarketers know this?

Don't answer that.

"I'm usually pretty chill and not much bothers me," said Mark Angiello, a 29-year-old office manager from White Plains, New York. But the one thing that really gets under his skin, that he "hates more than anything else in life" is the horrendous one-word message – "K."

So... wait... we're supposed to, on the one hand, condense our texts into emojis and "u" for "you" and acronyms such as IDK or LOL or whatevs, but you're going to get pissed because someone typed "K" for "OK?" Good gods.

Twitter user @Ryannlawrence writes, "If I give you an emoji in a text, you have to give me one back. Those are the rules. "Twitter user @Zelvel writes: "It's an unsaid rule in texting if you weren't the last person to send a text before you fell asleep, you should be the first to send one in the morning."

Neither of these "rules" make any sense whatsoever and this is why I despise and avoid Twatter.

Other examples include don't leave a message after the beep...

If you don't leave me a voicemail, and you're not on my contacts list, I will not return the call. Period. To be safe, leave a gods-be-damned message, even if it's just "Hey, it's ***. Call me back."

...don't send too many texts in a row...

Two? Five? Seventeen? 42? How many is too many, you unutterably idiotic prat?

...and don't just start a conversation with "Hey."

How about "yo?" Does "Yo!" work for you? Thor's balls...

"These rules are simply a new manifestation of a phenomenon we've seen in the past," said James Ivory, professor of communication at Virginia Tech.

All due respect to Virginia Tech (I'm a UVA grad; that's a joke), but are you being descriptive or prescriptive here?

So, not everyone gets the memo.

Oh? Maybe you should have texted me to find out if I got the memo. Oh, wait, you can't. Look, you might be thinking this is an "age" thing for me, or a "technology" thing, but no. For me, it's a refusal to conform to social norms until a) I know what the freaking norms are and b) I have internalized a damn good reason for conforming.

"As soon as people aren’t talking face to face, the first thing that gets lost is some of the richness of the nonverbal communication," Ivory said.

Or you could, you know, learn how to frakking write. But I suppose if everyone knew how to write, writers would be out of a job. Not that most of us have that job, anyway.

"People immediately fill that gap by trying to approximate it," either by using emoji, adopting informal etiquette or sending gifs – those animated images that seem to sum up a sentiment in seconds.

You mean like this?

So, okay, now the article gets to the inevitable numbered list that makes it clickbait. As usual, I'll just highlight a few select items.

2. One word texts like OK and LOL are conversation killers. Don't respond with one word, unless you don't want to talk anymore.

K.

6. Don't ask for likes, comments or shares.

This one, I can actually get behind. I don't believe I've ever done it. My posts - such as they are, avoiding Failbook and Tweeter - need to stand on their own. And as a rule, I never like or share if you beg for it. It's like begging for a kiss; it makes you look desperate and lonely. But hey, if you ask for comments, as long as you're not begging, okay, I can sometimes accommodate that.

8. You don't actually have to leave a voice message.

As I noted above, yes. Yes, you really do. If you want me to get back to you at all.

14. If you don't get a response, you don't have to get angry. It's not always that big of a deal.

Anyone who gets angry when I don't respond immediately gets ignored forever. I sleep at irregular intervals, and I turn my phone volume off when I'm napping, lest I be woken by an "urgent" robocall. If I don't respond, it's because I was asleep. Maybe I'll miss something important like a new beer release, but so be it.

Anyway, what all of these boil down to is the usual: be mindful of others. Hell, even I can do that (most of the time, anyway), and I'm generally known for having no shits to give. I don't need vapid internet articles that mostly quote Twunter users and professors at second-rate colleges (

) to tell me that.

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