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:

Turkey DrumStik

about 9 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

October 21, 2018 at 1:01am

#943866

Re: Generations

I'm getting more than a little tired of crap like this:

https://www.nbcnews.com/business/consumer/weddings-cheese-radio-what-will-millen...

This just in: the popularity of things waxes and wanes over time. Film at 11. (That's an old-person reference.)

Actually, the whole concept of "generations" irks the living shit out of me. Baby boomers, Gen-X, Millennials, whatever. It might as well be astrology. "Aquarians are killing meat!" "Capricorns are killing Christmas!"

For example: most of the definitions I've seen put Boomers ending with people born in 1965 and Gen-X ending in 1985. If you go by this, then someone born in 1966 would have more in common with someone born in 1985 than they do with someone born in 1965. Similarly, someone born in 1985 would have utterly different interests and experiences than someone born in 1986.

This is obvious nonsense.

Okay, sure, we're all products of the times we grew up in. But that doesn't mean we're stuck in them. Sure, I didn't have a personal computer until I was 12, and mobile phones weren't a widespread thing until I was fully an adult. But that doesn't mean I didn't embrace these technologies wholeheartedly. And yes, I like a lot of music from the 70s, but I also like a lot of music from the 90s and noughties. And the 60s. And the 50s. Good music is good music and doesn't have a "decade." And bad music will always be bad music, like 90% of the horsefarts they forced into our earholes in the 80s. Music to me isn't so much about how it fit into my life but about whether it's a good song or not (which I'm aware is somewhat subjective, but the point is it has nothing to do with the release date except in terms of its historical context).

Also, people grow up, they get older, they retire, they die. Usually in that order. They're still freakin' people. There will always be fads and trends as long as there are people around to follow them, and young people have always had different interests than older people.

I don't know if this is just a marketing thing gone rogue, or if some shadowy cabal is trying to find another way to keep us divided and unsatisfied, the better to sell whatever they're selling, but seriously, it needs to stop. Bad enough they've wedged liberals and conservatives apart to the point where we're literally killing each other; all we need now is for "Millennials" to get so pissed at "Boomers" that they'd rather implement euthanasia than deal with taking care of the elderly.

So, give it a rest. Old farts, stop kvetching about "kids these days." (I reserve the right to do so ironically, of course.) Kids, stop blaming Boomers for wrecking the planet. And for fuck's sake, don't fall for marketing hype.

4 Like • Comment • View 2 comments

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