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 5 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

December 24, 2018 at 12:18am

#948084

Millennials Killed Millennials

https://www.theatlantic.com/ideas/archive/2018/12/stop-blaming-millennials-killi...

The American system has thrown them into debt, depressed their wages, kept them from buying homes—and then blamed them for everything.

No, idiots. The American system didn't do that last bit. The media did. And you're part of the media.

The entire concept of demographic "generations" annoys the shit out of me. And it only gets worse as time goes on and I read more crap like this.

Just think about it for a couple of minutes. You have someone born in, say, 1986, supposedly an early year of the "Millennial" generation. And then you have someone born in 1983, supposedly a late Gen-X. You're telling me there is, somewhere in '84 or '85, a hard cut-off, where someone born one day is Gen-X and someone born the next day is a Millennial? Hell, you can even imagine identical twins, one born during the last seconds of Gen-X, and the other born in the first second of Millennial.

On top of which, you'd have to convince me that our 1983-born X-er has more in common with someone born in 1966 than with someone born in 1986.

It's fucking astrology, is what it is, and without the interesting math involving apparent planetary motion.

I look at it this way:

There has always been, and always will be (at least until the inevitable apocalypse), a continuum of ages. In any given year, a wide variety of people were / will be born. A sharecropper's kid has very little in common with a trust fund baby. Two people in the same socioeconomic stratum can also be as different as heads and tails on a coin. There is as much variation within a group of people born in a given year than there is between groups of people born 25, 50, or even 75 years apart.

Also, some things suck and other things get better. This is due not to a single "generation" or cadre of ages, but every single person doing his or her own thing.

And attitudes change over time. There's nothing new about this observation. But people pick up different attitudes depending on their upbringing and the stories to which they're exposed. And who does the upbringing, and the story-telling? Older people, subject to their own biases. Yes, ideas evolve. No, you don't get to blame an entire cohort for that.

I'm pretty sure the whole "generations" thing is just another way to divide us, like politics or countries. It distracts us from the real issues, which we can either work to solve, or ignore, depending on one's individual preference.

Sure, there are going to be differences between someone like me who remembers (barely) the first moon landing, and someone who grew up sucking on an iPad (which, incidentally, has exponentially more processing power than the Saturn V did). But let's not fool ourselves: for as long as there has been civilization, old people and young people have complained about each other, and yet people continue to produce young people like there's no tomorrow (in fairness, there might not be).

So you know what I want to see Millennials finally kill?

Generations.

Fly, my pretties!

5 Like • Comment • View 3 comments

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