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:

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

1 Like

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

October 30, 2021 at 12:02am

#1020407

Scare Tactics

Wouldn't you like some new monsters for Halloween?

5 Creepy Creatures And Nightmare Fuel From Foreign Folklore

Monsters help us face our fears, but familiarity with them takes the edge off... which is usually a good thing, because it means that the fear is no longer controlling us.

You might have heard of some of these shards of nightmare, or you might not. I don't have much else to say about it, because I'm still recovering from some dental work I had done the other day. Speaking of fears. (Not one of mine, actually. Eye surgery is. And that's now scheduled for December.)

Monsters are like porn. There eventually comes a time when you get bored with the normal stuff like vampires, zombies, or werewolves and want to spice things up a bit. And whether you're looking for new ways to scream or cream, your first stop should always be foreign countries where you can easily find stuff that was deemed too extreme for the US market...

And since it's a Cracked article, it's a numbered list in descending order.

5. Ushi-Oni And Nure-Onna: Japan’s Damned Double-Act Of Doom

The description of Nure-Onna (or Wetty Betty, if you will) differs from region to region. Sometimes she's human from the waist up with a monstrous snake tail where her legs should be, like H.R. Giger's take on The Little Mermaid, and sometimes she's just a head on a snake body. However, Nure-Onna can use magic to make herself appear as a human woman holding a baby. And that's how she gets you.

Thankfully, that wouldn't work on me. I just assume anyone holding a baby and looking for help is some sort of scammer, and I back off and call the cops. Let them get sucked into the Nure-Onna's dark designs instead.

Once she spots her victim, she magics herself into a mother in distress, calls for help, and then asks you to hold her baby while she pops to the store for some diapers or whatever. And then you're left raising the kid until they're 18! AAAAHHHHH! The horror!

And yes, that disturbs me on a deep level, more than the whole "trapping you while the snake woman eats you and drinks your blood" thing.

Same as Nure-Onna, Ushi-Oni likes to live near the water and loves having people for dinner together with Dame Judy Drench but what's weird is that no myth explains WHY. Like, Nure-Onna does all the work luring in people and all that, yet she allows the Cow Spider to join her. This leads us to only one logical conclusion: the two are banging. Now try to imagine what that looks like (and then try aiming for the trashcan.)

I mean, really, for the full effect you'll need to click on the link, which has drawings. Go on. You know you want to.

4. Slavic Female Demons Sound Like An Excuse For Horrible Domestic Abuse

Really? Because to me that sounds like the name of a hard metal Go-Gos cover band.

Women could become a boginka, dziwozona, or mamuna by dying in childbirth, committing suicide, or killing their child. After the transformation, they liked to target young women, kidnapping them and beating them with sticks, dunking their heads in mud, and twisting their arms before ultimately returning them home … Which really sounds like a weirdly convoluted, ancient-Slavic version of "I walked into a door."

For some reason, I've never heard stories about these. I wonder why.

A lot of the myths surrounding Slavic female demons were actually meant to explain the difficult/unfortunate parts of life in a time when medicine boiled down to: "Sounds like you have goblins in your blood. Here's some vodka."

Amusing as that is, vodka was a relatively recent invention in human history.

3. The Pishtaco Are The Embodiments Of The Andes’ Colonial Trauma

I'll give you a few minutes to laugh at the name "pishtaco," which I suggest you do because things are going to get super gruesome super fast after that. So enjoy yourself while you still have time.

They're not kidding here.

"Pishtaco" comes from the South American Quechua-language "pishtay," meaning "to cut up/slaughter," and refers to a particularly effed up kind of vampire: one that steals your fat.

Sounds like something a lot of us could use.

The reverence of fat actually goes back to the dawn of human civilization, but the people of the Andes took it in a particularly disturbing direction with the stories of the terrifying pishtaco.

I'm betting it goes back longer than that.

The "pishtaco" boogeymen were created after the people of the Andes ran into Spanish conquistadors in the 16th century and saw them using the fat from slain enemies to treat their wounds.

Just when you thought colonialism couldn't get any worse.

2. Tupilaq Is Greenland’s Blowjob Frankenstein

Or a rapper. A rapper with an album called "Blowjob Frankenstein."

Seriously, though, you're going to have to read this one for yourself.

1. Tokoloshe: Like A South African Graboid … Only Smaller … And Actually The Penis Of A Goblin

Hm. Story idea: Combine 1 and 2.

You're welcome.

But again... I have a content rating to consider, so you're just going to have to read it yourself.

Or not. I totally understand "not."

In any case, it's probably too late to dress up as any of these for Halloween. Or, perhaps, there is no such thing as "not too late."

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