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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 12, 2024 at 8:41am

#1079840

Blond Man's Bluff

Sometimes, I link to Cracked for its take on serious topics. Sometimes, though, it's because of jokes.

The Funniest Blonde Jokes Ever Told

Historical blonde jokes aren’t as well-documented as other classics, like fart jokes, for example.

Fart jokes may be "classic" (the oldest recorded joke is one of them), but they are the lowest form of humor, unlike highbrow amusements such as dead-baby jokes.

The people who study this type of thing tend to agree that they’re just lazily recycled versions of older jokes, that replace racism and xenophobia with sexism.

Yeah, not exactly a step up.

But the genre does have some notable subversions!

The thing about subversion is you need to be familiar with the thing that's being subverted, and hardly anyone tells blonde jokes anymore, so some people might not get the twists.

5 ‘The First Officially Recorded Dumb Blonde’

This is included for historical context.

Catherine-Rosalie Gerard Duthé was a French nun, ballet dancer and courtesan in the late 18th and early 19th centuries.

We should be concentrating on French jokes, not dumb blonde jokes.

She had a particularly notable habit of “pausing for extended periods of time before speaking.” Some might call this act “thinking,” but the French decided this made her dumber than a beret full of baguettes.

One wonders whether this contributed directly to the French Revolution.

4 Meta Blonde Jokes

You know how a blonde joke works. A brunette, a redhead and a blonde do something, the blonde does it wrong, because she’s dumb and incapable, the patriarchy grows stronger.

Worth going to the link just for the joke here.

3 The Counter-Revolution

A notable, though flawed, early ally was cartoonist Murat Bernard Young, who drew two extremely popular comic strips. Dumb Dora was about a space cadet brunette, while Blondie was about a smart, capable mother whose husband was the bumbling, glassy-eyed doofus.

The "bumbling, glassy-eyed doofus" trope continues to this day (Homer Simpson, e.g.), but apparently, it's okay to make men look stupid.

2 Existentialist Blonde Jokes

The New Yorker’s “Existentialist Blonde Jokes,” written by Alex Baia back in 2021, subverts some of the most tired blonde jokes out there...

I rag on The New Yorker on a regular basis, because it's pretentious as fuck, but one thing it's usually gotten right is comedy. I'll just copy one of the jokes here:

How do you drown a blonde?

Remind her that life is inane, repetitive and intrinsically meaningless.

1 Blonde Jokes for Men

Ever wonder about the difference between blonde and blond? It's not like gray/grey, which is largely a difference in US and UK/Commonwealth English. It's because "blond(e)" is French, so it possesses grammatical gender. Women are blonde; men are blond. It's one of those few words we stole from French that kept its inflections, like fiancé/fiancée.

Anyway, like I said, there's no need to specify the man's hair color. Many of us don't have any, anyway, and we're all stupid and bumbling, regardless of coiffure.

1 Like • Comment • View 1 comment

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