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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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.

March 3, 2019 at 12:16am

#953597

Conspiracy

Sometimes, people do awesome things.

http://mentalfloss.com/article/575702/denver-international-airport-installs-talk...

Denver International Airport Installs Talking Gargoyle as a Nod to Conspiracy Theories

The scariest parts of most airports are the long security lines and baggage fees. At the Denver International Airport in Colorado, travelers are also confronted with disturbing art, strange markers on the ground, and a demonic horse statue that killed its creator (no, really). These quirks have given rise to conspiracy theories that the airport is a center of illuminati activity, and now Denver International is leaning into these rumors with a new gargoyle that talks to customers, the Denver Post reports.

Hey, if you're going to be a target for conspiracy nuts anyway, might as well OWN that shit.

As an aside, "theory" isn't a good word for this sort of thing. But then, English has an unfortunate, stubborn reluctance to mold itself to my will. It is unlikely that the conspiracy whackjobs will adopt my suggestion of "conspiracy fiction," "theory" it will remain.

I may be playing into their hands to give this sort of thing any attention at all, but again, it's not like anyone spares a thought for my opinion about these things. Thus, I can safely learn what the fringe element is concocting, knowing that I can neither fuel or dampen their fire.

When you think of people who honestly see conspiracies in every damn thing, the image you probably have involves a tinfoil hat. Some people believe that it blocks the mind-control rays. I've tried to start a counterargument that tinfoil hats actually concentrate and enhance the effect, thus blowing their minds, but again, nothing.

As the video below shows, the wise-cracking character didn't avoid bringing up the airport's reputation. "Welcome to Illuminati Headquarters … I mean, Denver International Airport," he tells one passerby.

That part made me LOL.

I find most conspiracy "theories" highly amusing. The ones I don't find amusing are the ones that put all our problems squarely on a single group of people, usually "the Jews;" that sort of thing just fuels more xenophobia, something we could do with a lot less of in the world. And also the moon landing hoax people - that group is beyond help. Even the flat-Earthers can be a source of amusement, but to reject the single greatest accomplishment of humanity is to reject humanity itself. I just want to take them to the edge of the planet and push them off.

The gargoyle is part of a larger campaign from the airport that embraces the conspiracy theories surrounding it. Last year, Denver International hung posters referencing aliens, freemasons, and lizard people outside an off-limits construction zone

Someone over there at DIA has an epic sense of humor. This, folks... this is how you troll.

3 Like • Comment • View 2 comments

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