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 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 15, 2018 at 12:45am

#941450

Constipation

I think I'm becoming evil in my old age. Well, more evil, anyway.

These past couple of days, I've been hearing about people who decided to ignore evacuation orders and stay in a hurricane zone.

Now, I'm a gambling man. But it's one thing to risk a few bucks at the blackjack tables, and entirely another to stay in a place that has a good chance of being flooded and/or blown away on the wind. Not that I don't understand, at least to some extent. Someone tells me to leave my home, hell, I might even make the same choice.

But then... then some of these people started asking for help. And that's where I draw the line. So I say: Fuck 'em. Now they've not only put their own lives at risk - their choice - but also those of emergency responders.

And then I think, well, there are at least three situations I can see where it makes sense to have a bit of empathy for their plight. One story I saw before the hurricane hit was a mother who stayed with her three children. Why make the children suffer for their mother's choice? They didn't decide to be born unto an idiot. And emergency responders made their choices, too.

Yeah, I know, the storm wasn't as bad as predictions indicated. But that could have gone either way, really. Like I said, a gamble. No sympathy for the stupid, here.

But my lack of sympathy doesn't stop there. Today, a retail clerk asked me if I wanted to donate to some children's charity. I refused. Then she rang me up and proceeded to try to get me to sign one of those little "I donated" signs they hang up in retail establishments. "I didn't donate," I reminded her.

"Oh, that's right," she replied, thus adding to the extortionist tactics in front of the other people in line.

I tell myself it's because I donate to whom I choose, when I choose, and I'd rather pick organizations that have low overhead so the money goes to actual victims, not charity organizers. But honestly, children's charities are at the very bottom of my list, behind disaster relief, pet rescues, and casino owners. Partly because of the overhead, yeah, but partly because I just don't give a damn.

I also turned off Amber Alerts on my phone because I simply don't care. I tell myself it's because I'm rarely in a position to do anything about it, and the notification is annoying, but I have weather alert sirens turned on in the damn thing because that could affect me.

Now the only real question is: can I live with being ethically constipated - that is, utterly failing to give a shit?

Maybe. We'll see. I do know I'm not actively seeking laxatives for it.

2 Like • Comment • View 1 comment

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