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 2 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 4 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.

January 27, 2023 at 12:01am

#1043725

Bizspeak

After a visit to the dentist, I'm on a course of antibiotics for a week because of a tooth thing. This means no drinking. 8 hours in. Send help.

Funny thing is, I go a week without drinking, no problem, quite often. It's only when they say I can't that my oppositional defiant disorder kicks in. Kind of like how I've never particularly enjoyed grapefruit, but as soon as I started taking a medication that forbids grapefruit, I started craving it. It's not even like I "can't" drink; it's just that alcohol negates the action of antibiotics, rendering them less effective (the precise opposite of what grapefruit does for statins).

Today's article has nothing to do with that, except that the subject matter is enough to make me want to drink more.

Let’s not circle back on that: These 10 corporate buzzwords are the most hated in America

“I’m just circling back to discuss how culture has changed within this new normal we’re in, hoping we can move the needle on this and think outside of the box.”

If I were playing the bizspeak drinking game, I'd already be passed out after that sentence.

But unlike talking about how it’s abnormally chilly out, no one really likes chatting in overused corporate phrases.

Apparently, many do. Mostly middle-management, I'd wager. It's been a long time since I was in an office setting, and even then it was a small office, and I still got subjected to the pin-putting and circling and such.

More than one in five workers dislikes corporate buzzwords...

See? The majority doesn't dislike buzzwords.

Below are the top 10 annoying phrases most hated among your coworkers:

You're damn right I have things to say about these.

1. New normal

This is probably a pandemic-related thing. Shit changes all the time, but the situation in early 2020 was more of a discontinuity than the usual gradual change.

2. Culture (e.g., “company culture”)

I'm not sure this is so bad as long as it's not overused [Narrator: it's overused].

3. Circle back

Pretty sure I remember hearing this one, and it annoyed me. The phrase that accompanied it was often "put it on the backburner," which annoyed me even more, especially when it referred to something I was working on.

4. Boots on the ground

There is no excuse for this unless you're literally fighting a war. And by "literally," I mean "literally."

5. Give 110%

I blame sports for this bullshit. The worst bizspeak, in my view, comes from sports. Even if this were physically possible, which it is not, are you going to pay me 10% more if I do this? No? Then I'm not going to do this.

6. Low-hanging fruit

As metaphors go, this one's not so terrible—unless it's overused [Narrator: ...sigh].

7. Win-win

Seriously, stop. Though it is nice to occasionally hear evidence that it's not a zero-sum game.

8. Move the needle

...once it's already jammed into your eye

9. Growth hacking

Okay, that's a new one for me, and it's legitimately enraging.

10. Think outside the box

The problem with the idea of thinking outside the box is that most people can't even think inside the box, which is a necessary first step. This is also known as "thinking." For example, say that your problem is you want to save money. The "thinking" solution is to find where you're spending too much money, and cut back. The corporate "thinking outside the box" solution might be to cut 1/3 of your workforce and make the other 2/3 do all their work without giving them raises. If you were really "thinking outside the box," though, you'd stop paying everyone and fuck off to Fiji.

Despite disliking buzzwords, three-fourths of respondents said that using these phrases can make someone sound more professional.

It certainly makes them sound more corporate.

But not all buzzwords are annoying. Preply respondents favored terms like “at the end of the day,” “debrief,” and even “sweep the floor.”

No, no, and no. Also no: "It is what it is." Make it all stop.

One in five respondents considered jargon in a job description to be a warning sign, with most noting that the language factored in their decision to apply or not.

You want to know what the biggest red flag is in a job description? I'll tell you. And it's not necessarily jargon. Here it is: "We consider ourselves family." If you see those words, or anything like them, in a job description, run. Run hard, run fast, and don't stop running until you hit an ocean. Then start swimming. Seriously. Every company that tells you they're "like family" is going to be just as dysfunctional as an actual family; or, perhaps, be an actual family that works well together—in which case you're going to be the Outsider and never quite fit in.

The main offenders for candidates were overly optimistic words that suggested an undercurrent of a more tense work environment, such as “rockstar,” “wear many hats,” and “thick skin.”

If you want me to be a rockstar, you'd better have the caterers ready to provide me with specialty cheeses and an olive bar. It's right there in my contract; didn't you read it?

This reminds me of the secret code of real estate listings, like "cozy" meaning "cramped," "private" meaning "in the middle of nowhere," or "vintage" meaning "draftier than a beer bar."

About the only positive thing I can say about these kinds of buzzwords is that they do make fine fodder for writing, especially writing antagonists. So it can be beneficial to learn them. Just remember, if you use them unironically, that means you're the bad guy.

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