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!

about 5 hours 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

about 7 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.

April 3, 2024 at 9:25am

#1067483

Sumer in the City

Thank Atlas Obscura for this one, which, again, I'm sharing mostly for the hell of it. Because it talks about two of my favorite things. No, not science and math; beer and food.

Ordering Off a 5,000-Year-Old Mesopotamian Menu
A community effort brings ancient flavors to modern Texas.

Texas has forfeited any claim to being "modern," but whatever.

Among the campus buildings at Rice University in Houston, Texas, one curious structure stands out... It’s called a mudhif, and for Iraq’s Marsh Arab ethnic minority, it’s a traditional village meetinghouse where disputes are settled and important gatherings are held.

What Marsh Arabs are doing in Houston is explained in the article.

Alrawi describes the dinner as a way “to complete the setting” of the mudhif by paying homage to the structure’s ancient origins. Rather than modern Iraqi food, the dinner menu is based on recent archaeological discoveries from Lagash. Located in modern-day southern Iraq, Lagash was a major Sumerian city home to some 100,000 people in the third millennium BC.

While that might not seem like a huge city by today's standards, I think it was quite a lot of people for 5,000 years ago. The far better known Babylon, in the same general area, might have reached 200,000, but that was several centuries later.

...the central grain was barley, used to make both bread and another Mesopotamian staple that the team in Houston set their sights on recreating: beer.

And now they're speaking my language.

Though the beer of ancient Mesopotamia bore little resemblance to the delicious magical concoctions of today, it was fermentation of malted barley. The article goes into some of the process.

“Whenever you put an archaeologist together with a chef or a brewer,” says Lao, “they feed on each other.” Recreating the Mesopotamian meal has been a team effort.

Now, that's an image I might have done without.

Also, as the article points out, it's probably impossible to faithfully recreate all of the recipes. Moreover, we're talking about working-class food, the ancient equivalent to street tacos, hot dogs, and the like. Food availability and price keeps changing; a commonly-touted example is that lobster used to be considered trash that only poor people ate, while now it's treated as a luxury item (I don't know how true that is). So do you recreate the food, or the experience? Lots of cultures have come up with their own working-class food, but the commonality there (pun intended, as always) is that it's all based on what's abundant and cheaply available.

At least until it becomes widely known as delicious, at which point it ceases to be working-class food. Like how you might pay $10 for a stadium hot dog, or how I pay $30 for a pizza.

But I feel like it brings history to life if they try to recreate the recipes with the foods then involved. Few people love memorizing the facts, dates, and minutiae of history, but get people together for a meal, and stuff will stick in their memories.

That said, I have little interest in trying original Sumerian beer. It's enough for me to know how the beverage got its start.

2 Like • Comment • View 3 comments

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