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!

a day 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.

October 30, 2019 at 12:05am

#968631

The King's English

Well, I've signed up for "30-Day Blogging Challenge ON HIATUS"

[13+] again, for November, since I'm not doing NaNo this year. Once again, I figure if I'm going to try to write something in here every day, might as well mix it up with some prompts I wouldn't consider on my own.

Meanwhile, I still have a ton of blog fodder to get through. Here's today's:

https://cheezburger.com/9184517/the-english-language-being-infuriatingly-confusi...

The English Language Being Infuriatingly Confusing (39 Images)

By "images" it means "screenshots of tweets." I despise Twitter with the fiery passion of 10,000 suns, but sites like this (as clickbaity as it is) can sometimes present the best of the worst.

Since they're screenshots, copy/paste isn't an option, so I'll just pick a few amusing ones to highlight.

#8 It blows my mind that english has no plural for "you."

Ah, but it does, at least here in the South. "Y'all" is a perfectly good second person plural. It sounds more polite than "youse guys" (NY/NJ) or "yinz" (specific to the Pittsburgh area).

Incidentally, it's always "y'all" and never (as I've seen it) "Ya'll." An apostrophe stands in for missing letters, and the missing letters in this case go between the y and the a, not the a and the l.

And yet, even if you avoid regional dialect and think only of Standard English, the plural "you" still makes more sense than the French "vous," which can be either a second person plural, or a formal second person singular. How do you know when you can drop the formal "vous" and use the familiar "tu?" I guess I'll have to spend some time in France to figure this out. Awww.

#9 Defenestration

Still one of my favorite words.

#11 Why does my nose run but my feet smell?

You might wanna see a doctor. Or three.

#22 I before E except when you run a feisty heist on a weird foreign neighbour.

Yeah, okay, that one's an example of why English is frickin' weird.

#26 The fact that Kansas and Arkansas are pronounced differently bothers me way more than it should.

This might have been my introduction to the fuckeduppedness of the English language. To this day, I pronounce Arkansas "ar-Kansas" just to be funny. I also pronounce Missouri "misery" because it's Missouri.

#33 Why is a "w" called a "double-U" when it is clearly a "double-V"?

Not in cursive. Also, because in Latin, from which we derive our alphabet, V is U. Confused yet?

Anyway, those are just the short ones. The longer ones are worth reading, too. I'm now even more convinced that English has been dominating the world stage not because of British colonialism or because it's versatile, but because once you learn English you feel a sense of pride unmatched by learning any other language (except, perhaps, Mandarin, though I wouldn't know). Once you've learned to navigate its dark corners, there's no going back.

3 Like • Comment

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