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 12, 2019 at 1:03am

#954178

Tequila! Women!

No, it's not what you're thinking. Jeeze, you people and your gutter minds.

https://www.cnn.com/travel/article/tequila-international-womens-day-mexico/index...

If not for women, there'd be no tequila

...It's here that casual sippers drink this aromatic spirit, but there's one secret they may not know: Without the women of Tequila, there'd be no tequila.

First of all, if not for women, there'd be no <insert name of anything humans create> because there'd be no humans to create it.

Okay, fine, the article is more nuanced than that.

Tequila, of course, is one of the cornerstones of civilization, along with whiskey, wine, and beer. You know what my greatest concern about climate change is? It's not the loss of coastal cities. It's not a greater incidence of extreme weather systems. It's not mass extinctions, decimation of the human population (actually, 1/10 is a conservative estimate), water insecurity, wars, desertification of food-growing regions, or even the loss of coffee. Y'all brought that shit on yourselves. No, it's that the particular climate required to grow blue agave will shift away from the Tequila region, thus cutting off my supply of tequila.

I can only trust that when this happens, Mexico will relax the laws to allow tequila to be made elsewhere.

You know what else has a long history connected specifically with women? Beer. You'd never know it today, as something like 95% of all microbrewers are bearded hipster dudes, and the macrobrewers are run by faceless, genderless corporations. But historically, it was women who brewed the beer, passing down secrets along with (presumably) beauty tips and advice on how to bag rich men.

To be fair, beer would work for both of those.

https://en.wikipedia.org/wiki/Women_in_brewing

From the 18th century onwards, women were increasingly barred from the business of brewing, except as barmaids or "publicans", licensees running pubs.

In ancient Sumeria, brewing was the only profession that was "watched over by a female deity", namely Ninkasi.

Yeah, I know this is a bit late for International Women's Day, but hell, why not make every day International Women's Day? Especially if there's beer and/or tequila involved.

Just don't expect me to do a Deadpool cosplay.

5 Like • Comment • View 1 comment

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