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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Turkey DrumStik

about 11 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

September 23, 2018 at 12:54am

#941886

Fall Down

I guess Fall is officially here. Or Autumn. Never did figure out why there's two names for it, when the other seasons only get one each.

A lot of people love this time of year. I am not one of them. Oh, it has its pleasures - Oktoberfest, leaf colors, and generally lower humidity among them - but the problem with autumn is that it's immediately followed by winter, and I despise winter in all its incarnations.

I don't like the cold, though I am rather fond of the darkness. A lot of people I know love the cold, giving me yet another thing that I don't understand about humans. If I hear one more "I can always put on more clothes, but I can only take off so much when it gets hot," I might lose it at that human in particular. No amount of clothing can keep my hands and feet warm in the cold, and when those things are cold, I'm miserable.

Gloves, socks, whatever - doesn't matter. Within seconds of venturing into the frigid air, I start to feel like an icicle. And yes, even someone who loves the indoors as much as I do has to venture out occasionally - and in the winter, occasionally is too often.

About the only good thing about winter as far as I'm concerned is that I get to wear my leather trench coat without getting too many dirty looks.

One strange thing, though: I'm a Birkenstock guy now. Have been ever since I visited Maui (which, I might add, I did in a February, the better to avoid the worst of that horrid month in Virginia). Birkenstocks are open-toed, cork-soled sandals. They're very comfortable once you break them in, and appeal to my basic (lazy) nature in that I don't have to tie shoelaces.

I wore them almost exclusively on the cross-country trip I took last December, and I noticed something odd: despite their sockless nature, I survived temperatures in the single digits (F) while wearing them in Nevada. Best I can figure is it's not just the cold that gets me; it's the moisture, which is notably absent in the desert.

Maybe I should move to Nevada. No... no. Too much temptation. Utah? Nah. Too little temptation. Thing is, I like Virginia - but mostly in the spring and summer.

Might have to visit Maui again.

2 Like • Comment • View 1 comment

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