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 8 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 10 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.

July 28, 2020 at 12:21am

#989336

Something is Rotten in Belgium

If anyone's joining us from "July 2020 Blogging Bliss Newsletter - Issue Ninety-One"

: Hi! Everyone else should definitely check out that link, because it features Me. Oh, and some other cool stuff too.

PROMPT July 28th

All month, you’ve been replying to prompts straight from the Challenge War Chest, filled with prompts from previous 30DBC competitors. Today, write three of your own prompts and then reply to one of them in your entry.

I had a disappointing experience yesterday. I've been walking to my local taphouse about once a week since they reopened (patio only) for some food and fine fermented beverage. Someone has to make sure they're still in business for the foreseeable future, and I volunteer as tribute. Anyway, yesterday was Taphouse Day for me. Among other libations, I ordered a Duvel

, because whenever a Belgian beer shows up on draft, I jump on that sucker.

What I got wasn't a Duvel. I know what it's supposed to taste like, and it was just... off. Didn't even taste Belgian. Maybe they got a bad batch, or they mixed up the taps, or something. I also considered the possibility the fault was in my own palate -- sometimes beer just tastes different if you eat certain foods or drink something else first -- but none of the other beers I tried were wrong. Besides, the trademark feature of a Duvel (and a few other Belgians) is a particularly creamy head, and this one was as headless as a horseman.

Only mildly disappointing, to be sure, but I mention it because in all the years I've been a craft beer snob, this is the first time I could tell that something just wasn't right. Well, there was the time a brewer in Colorado had me try what he called an IPA, and I was like, "This isn't bad; it's more like an ESB." "Oh, yeah, it is an ESB but Americans think it'll be bitter, so we call it an IPA." For the record, ESB is "Extra Special Bitter," but the style isn't bitter at all, while IPA (India Pale Ale) does tend to be bitter, so... I mean... what? They're both British styles. Leave it to the Brits to call malty beer "bitter" and label their own invention "India." (There's a story behind that but... later.) And leave it to the Yanks to call a thing something that it's not in an effort to sell more of it.

So, whatever, I had some other good beer and a nice stagger back home, marred only by my neighbor's Rott trying to kill me.

Point of all of this is that yesterday's experiences inform the three prompts I'm supposed to come up with today for the 30DBC.

1) Have you ever been attacked or threatened by someone's pet or a wild animal? If so, what happened? If not, what do you think you'd do?
2) What's the longest distance you've ever walked in one go?
3) Describe a time when you expected one thing and got something else.

I know I only have to talk about one of them, but:

1) The Rott today. I just stood on the sidewalk and stared him down. I was just sober enough to know that dogs take that as a challenge, and just drunk enough not to care. Come at me, mutt. His human corralled him, though.
2) I talked about yesterday. Worked out to something between 6 and 7 miles. The walk to the taphouse is only like a mile and a quarter (seems like more when it's 100F outside, though). If you're a kilometer/Celsius person, do the math; I can't be arsed right now.
And since I've already talked at length about (3), you can read about it above.

6 Like • Comment • View 9 comments

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