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!

4 minutes 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.

Adherennium Plotting something

about 2 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.

May 17, 2024 at 10:59am

#1071264

Mincing Around

Looks like someone gave Cracked a makeover. The most obvious change is that their logo no longer resembles that of the second-rate Mad ripoff they started out as. Not changed: countdown lists.

5 Words We Only Use Because the Old Ones Were Too Dirty
People only started talking about light meat and dark meat because they were too embarrassed to talk about breasts and legs

Yeah, and now "light meat" and "dark meat" have sexual connotations, because humans can be assholes. (When I was a kid, they called it "white meat," which I suppose comes with its own dark connotations.)

A friend is getting married, and you open up their gift registry. You see a “Dutch oven” listed there, and you suppress a giggle.

No, I don't, because 1) All my friends are past the "gift registry" stage and 2) I don't find the dirty version amusing in the slightest.

Later, at the ceremony, you deliver the toast, and you mention your Dutch oven observation. This angers and confuses people, who have no idea what you’re talking about. You are expelled from the venue.

As some people here can attest, my wedding toasts are simultaneously funnier and more cringeworthy than that.

5 Light Meat and Dark Meat

Light meat and dark meat are two different kinds of flesh on a bird. Confusingly, these names have nothing at all to do with white meat and red meat — all poultry is white meat, but some is light while some is dark.

And yet, we manage to infer the intended meaning from context.

Dark meat is fattier than light meat and arguably tastier.

Not to me. You could say I'm a breast guy.

But today, “light meat” and “dark meat” also sound sexual, so let’s just say whatever’s easiest.

Like I said.

4 Rooster

If we’re talking chicken double entendres, we of course need to talk about cocks. The cock is the male chicken, otherwise known as a rooster.

Honestly, this one's so obvious, I feel like the author got lazy.

3 Missus

The title in front of your name may reveal your gender, marital status, profession or level of nobility. The most common one for men is Mr., while women have Mrs., Miss and Ms. “Mr.” is short for mister. “Miss” isn’t short for anything. “Ms.” is pronounced miz but doesn’t represent any word other than “Ms.” itself. As for “Mrs.,” that’s pronounced missus of course.

And don't get me started on how some women take serious offense at being called "ma'am." In the US, this seems to be a North vs. South thing, though it's unlikely to start another Civil War. No, we have other things that will cause that.

2 Canola Oil

A lot of our vegetable oil comes from a plant named Brassica napus. The common name for this plant is rapeseed, with the “rape” part deriving from Latin word for turnip.

I'm almost sure I've written about this before, but I'm not about to put "rape" into the search box to verify.

1 Rabbit

Rabbits used to be called “coneys.” You’ll know that if you’re a fan of Lord of the Rings, in which Sam assures us that cooking a rabbit in a stew is the “one way to eat a brace of coneys.” He pronounces the word “cone-y,” the same way we pronounce Coney Island today, but originally, this word was pronounced “cunny.”

In the 16th century, “coney” became a pet name for women. Meanwhile, people already had the Latin word cunnus for “vulva,” which also gave rise to such words as cunnilingus and...

...couldn't they find a way to do this without typing the next word?

(Look, there's no reason why I can't say "cunt" once in an entry, but the opportunity to make the "couldn't" pun was overwhelming to me.)

Anyway, this is similar to why we don't call cats "pussy" anymore, except to set up or follow through with jokes. For example, long ago, Zsa Zsa Gabors was on The Tonight Show, way back in its heyday when Johnny Carson hosted. She came in with a cat, which perched on her lap.

Gabor: "Would you like to pet my pussy?"

Carson: "I'd love to, but you'll have to remove that damn cat."

...well, actually, that never happened.

But it's still funny.

3 Like • Comment

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