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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

August 28, 2024 at 12:20pm

#1075828

Fact-Ory

I promise I have more articles in the queue from not-Cracked than from Cracked, but sometimes, the RNG likes to cluster things. I should probably mention that there are images in the article that may get you called in to HR at work, but that'll probably happen anyway, just from wasting your time reading this blog and a dick joke site.

5 Simple Science Questions We Bet You’ll Get Wrong
What is a day? What is the Earth made of? You don’t really know

Yeah, I get it. There's a lot I don't know. There's probably even some stuff I get wrong, though I try to fix that when I become aware.

Phrasing aside, though, as usual, the article has an interesting take on things.

Between time travel, fusion reactors and the brain transplants we hear are happening any day now, science can sound like an intimidating set of disciplines.

I don't know about brain transplants, but I did see something recently about a brain implant for thought-to-text.

No, not Muskmelon's crazy stunt; this one seems legit.

Of course, I immediately saw the potential to reverse this so that advertisers can pay to have their product beamed directly into our brains. And you know damn well that's going to happen, along with people using it for porn.

Today, however, let’s set aside the most complicated theories and applications.

Porn isn't that complicated, unless you're doing it in space.

5. How Many Minutes Does Earth Take to Rotate Once?

Oh, I know this trick question. A solar day is not the same as a sidereal day.

The Earth takes 1,436 minutes for each rotation. Or, it takes 23 hours, 56 minutes and 4 seconds.

The article explains this in good-enough detail, but the simple explanation is: that's how long it takes for the same distant star (that is not the one we're orbiting) to reappear in the same place in the sky, relative to any point on the earth's surface.

But also, that sort of knowledge makes people like me fun at parties, but doesn't much matter for our 24-hour-everyday lives.

4. Would It Be Sexy to Have X-Ray Vision?

No.

3. What Color Is the Sun?

Another trick question, and also involving the accursed daystar.

The Sun is yellow, say most people with eyes.

Except when it's red or orange.

People who know more about space might offer a different answer. The Sun is actually white, they’d say.

Again, details in the article, but basically, white is what happens when you mix a full spectrum of light colors together. And of course the sun has a full spectrum, else we wouldn't sometimes see rainbows. (I may be mixing up cause and effect; our eyes evolved to see that range for reasons).

But to confuse us even further, physicists refer to the kind of photon emissions from the sun as "black-body radiation," for reasons I won't go into but you're free to look up. So maybe the sun is "actually" black.

2. What Is the World’s Most Common Substance?

Oh, that's easy: Stupidity.

What is the most abundant material on Earth — or rather, what is the most abundant material on or in Earth?

Um... advertisements?

Is it rock? Sure, but you’re going to have to be more specific than that. Anything can be considered rock.

Well, maybe not smooth jazz.

The most common substance in the world is in fact... bridgmanite. We’ll forgive you for never having heard that word before since scientists only got around to naming it within the last decade.

Yep, okay, you got me. Never heard of it before this. My knowledge continues to expand, thanks to a juvenile humor website.

1. Should You Shoot C-4 Explosives, for Fun?

I'm a big fan of doing lots of things for fun, so... yes?

On the other hand, if you answered “yes” because explosions are cool, we have bad news. The C-4 will not explode, so shooting it might be quite boring.

Awww.

Yeah, my understanding was the whole point of C-4 was to have a stable explosive. Which sounds weird, but you want it to blow up when you want it to blow up, not while you're transporting it to the thing you want to blow up. So it requires a detonator or whatever.

Shooting Tannerite,

now... yeehaw!

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