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 9 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 11 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.

February 6, 2022 at 12:02am

#1026120

It's Beer, Isn't It?

Another blind quote from "Journalistic Intentions"

[18+] -- again, I don't recognize where this comes from other than that it's a song, and I'm responding without looking it up.

"It's the power that gives you the strength to survive."

Oh! It must be about beer!

Not knowing the source of the quote -- and boy am I going to kick myself if it turns out I recognize the song -- I think it's fun to speculate.

A literal reading would lead one to believe the antecedent to "it" would be food. After all, food is power, and if you don't eat it for a while you won't survive, and it keeps your strength up. Or maybe solar energy, because without it, we'd all weaken and die frozen. Or, I know! Money. Money gives us the strength to survive, and with it you can buy food. Still, I like beer as an answer better.

Knowing pop music, though, it's probably talking about love or faith or some bullshit like that. In which case it's demonstrably untrue, because I've lived without love for a very long time and without faith for a whole lot longer and, well... here I am, chugging along just fine.

Maybe it's not pop music, though. Maybe it's experimental surrealism, in which case "it" could be something like the color orange, or perhaps wombat poop. Or would that be not surrealism but cubism? Okay, that's an obscure joke on several levels, but I'm sticking with it.

I wonder what cubist music would sound like (other than wombat shit)? I mean, anything can be surreal, not just art, but cubism is kind of purely a painting thing. And maybe sculpture; I don't know. Maybe someone will need to invent cubist music. I'm certainly not qualified to do so.

"Knowledge" could work too. After all, it's well-known (however clichéd) that knowledge is power, so that could be the answer to the riddle.

People like to make fun of the song "I would do anything for love (but I won't do that)" (written by Jim Steinman, sung by Meat Loaf) because they apparently can't figure out what "that" is, even though it's right there in the fucking lyrics. Just goes to show, people don't listen to lyrics. They should, though. The good ones (such as anything written by Steinman) are poetry; the bad ones mean you're listening to a bad song and you should feel bad for liking it.

In this case, though, the elusive antecedent to the neuter pronoun may be explained in the full lyrics to whatever song that is (I'm sure someone will tell me, or I'll finally get curious and look it up myself), but that's irrelevant to this entry, which is mostly just me writing down whatever thought comes into my head.

Oh! That's it! Thought. Thought is the power that gives me the strength to survive.

Nah... it's really beer.

5 Like • Comment • View 2 comments

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