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 a minute 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 2, 2024 at 11:19am

#1070406

Butt Of Course

As luck would have it, we get another Cracked link today. I don't really know why I saved this to my queue other than thinking, "You know what my blog needs more of? Juvenile cringe humor."

5 Horrible Things That Happened to People’s Butts

These are, of course, horrible, and not humorous at all.

Stories tell of a boy in China who was impaled by an office chair. This chair was powered by a gas cylinder, and the cylinder exploded in 2009, blasting metal up his butt and killing him.

Could have been worse. Could have been a couple inches forward and not killed him.

We don’t want to spend too much time on that story, on the technicality that it’s likely completely made-up.

Almost certainly an urban legend, but you just checked your office chair, didn't you?

5. Bullion, Milk and Whiskey Up the Butt

I will admit to being somewhere in adulthood before I realized that bullion and bouillon were two different things. So I understand getting it wrong Both words come from the same root, a French word that translates to "boil," meaning like heating something to the point that liquid starts to turn into gas, not the painful pimply thing you get on your butt.

Had to relate it to butts somehow, in honor of the article.

Point being, they stuffed bouillon up the butt in question, not bullion, which would have made it harder to insert the milk and whiskey. Editing is dead. (The text in this section gets the spelling right.)

President James Garfield died in 1881, after an escaped lunatic shot him in the arm and back... He died, historians now say, not just from the bullets but from how the doctors treated him.

I'd heard this before, but purposely avoided all the details... until now.

They shoved liquified food up his butt — beef bouillon, eggs and milk, along with whiskey and opium. They couldn’t let him eat, they said, because the bullet might have perforated his intestines (it really hadn't).

See? They got "bouillon" right there, but made up for it by misspelling "liquefied." (In fairness, that might be an alternate spelling and not an incorrect one.)

As a final note on this, let's not take this to mean "don't trust medical science." I mean, sure, don't trust 19th-century medicine; we might have advanced somewhat in that area since 1881.

4. Bitten by Your Own Attack Dog

I can't do this one justice (pun intended, but you'll only get it if you read the actual link); you'll have to see the article.

3. Filled With Compressed Air

No, not the way you're thinking.

McCormack didn’t wind up with a hose nozzle up his anus through debatable means. McCormack fell on a hose, and the fitting ripped through the muscle of one buttock, which is an experience no one would desire.

I don't know about that; it's probably a whole subgenre of paraphilia.

This was a compressed air hose, connected to the brakes in his truck, and the air now flowed through the hose, entering the man.

Ow. Ow. Ow.

He felt like he were blowing up like a balloon. But he survived, and he’s now available for interviews about how the working class is dealing with inflation.

Oh, that's right: that one line is the actual reason I saved this article in my queue. I'm mad that I didn't think of it first.

2. Water Ski Douche

No.

But it only gets worse:

1. Cooked as Steaks and Fed to Children

Someone's been reading too much Brothers Grimm.

Knight went on to be the first woman in Australia to be sentenced to life without parole. Authorities have no firm advice on how to stop something like this from happening again.

I have some, hard-won from personal experience:

1) Don't go to continent/island/countries where it's well-known that everything, including scorned lovers, is out to kill you;

2) Don't stick it in crazy.

3 Like • Comment • View 1 comment

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