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

September 21, 2023 at 10:18am

#1056034

Cold Reading

Might as well call this "How To Stop Being Awkward."

How To Read The Room Like A Pro
Reading the room is about seeing and hearing what’s both spoken and unspoken. And it’s a skill well worth mastering.

Lots of skills are well worth mastering. That doesn't mean we have the time, patience, or opportunity for all of them. For instance, to practice reading a room, one would have to repeatedly go out among people.

You walk into a conference room, dinner party, or group of playground parents and make a comment that immediately shifts the ballast of the conversation. Eyes dart at you. Their message is clear: Dude, read the room. But you’ve already said or done something out of sync with what’s appropriate in the moment.

Despite what I said above, I do go out among people from time to time, or at least I used to. While I can't say I've never embarrassed myself, I do think I have some skill at reading body language and facial expressions. Conversely, though, I've sometimes been one of the people saying, "Dude, read the room."

Learning how to read the room is an important skill, one that can be honed by pausing to observe a few key details.

No time for that. I have jokes to tell!

Think about if you’re home alone. You know that you can act a certain way, i.e., wear no pants.

I think I'm one of those weirdos who just feels better, even at home alone, wearing pants (well, sweatpants, but whatever). And a shirt. And a hat.

If company is there, you know enough to put on clothes.

Not if I want them to go away.

You want to practice, and like with a recipe or golf swing, you can get better if you invest the time. Find a partner who’s willing and will provide honest feedback.

"Find a partner." Right. Like that's easy.

Look at how people’s shoulders are angled. Then notice where their chests are pointing.

For fuck's sake. I've spent all of my adult life, and teenage years, forcing myself to NOT stare at half the peoples' chests.

You also want to notice people’s expressions as you listen to what they’re talking about, keying in on the paraverbals — the cadence, tone, volume, pace.

Hey, I learned a new word! If "paraverbals" is really a legitimate word. My browser underlines it with that squiggly red line.

It’ll take time, and you’ll make mistakes but because you’re trying, they’re usually non-fatal.

That's too bad, because if it's non-fatal, you spend the rest of your life waking up in a cold sweat at 4 am going, "Goddamn, I wish I hadn't said that."

Anyway, there's a lot more at the link. To me, it highlights the dangers of dealing with people. Fortunately, I've made enough mistakes of that sort that I never get invited anywhere anymore. Things are much easier online, and I'm all about easy.

4 Like • Comment

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