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 20, 2021 at 12:02am

#1017739

Ten

The pace of society sometimes moves too fast, and we don't always understand when the rules change.

Ten new commandments for modern life

So I present to you these fifteen *crash* er, TEN commandments.

Well. Some of them, anyway. You'll have to go to the link to read the others. Be aware it's a British site, but most of them are applicable to life in the US as well.

Thou shalt use thy indicators when driving for other motorists art not able to gaze into the intent of your soul, knobhead.

Good to see this isn't just a US problem. I guess they have BMWs over there, too.

Buy thee not the Mail nor the Sun, for loathsome rags are they that doth inspire hatred in their readers for their fellow man. Nor is exempt the Guardian.

Come on, now, the Guardian doesn't completely suck.

Honour thy waiters and waitresses, for they doth not deserve to put up with thy bellendery. Yea, and honour them in cash so the chain takes not 20 per cent.

Hm. I was led to believe that tipping was mostly a US insanity. Either way, servers are hono(u)rable people and surely they'd report even their cash tips to comply with the laws, right?

You can look up "bellend" on your own.

Worship not the false idol of your phone while in the cinema for it distracteth from the movie, nor discourse with thy neighbour, nor munch loudly on sustenance.

You know, commandments like this one make me extra glad to live within walking distance of an Alamo Drafthouse Cinema. Do that crap in an Alamo and you get kicked right out.

Send not dick pics to anyone unless they specifically requesteth them, which they shall not.

Oddly, I got that request once. I still didn't oblige. You wanna see it that bad, buy me drinks first.

Neverspoons, verily.

Okay, this one I'll have to explain for the non-Brit readers, but I may get something wrong because (surprise) I'm not British. As I understand it, Wetherspoons is a massive UK/Ireland company that runs pubs. Lots of pubs. What's wrong with pubs? Nothing. It's just that Wetherspoons is, like, the Squall*Mart of pubs. Support local businesses, especially those that are providers of the Holy Nectar. Worse, the higher-ups in the company supported Brexit, and don't get me started on the bullshit they pulled during the pandemic lockdowns.

I also have it on reliable authority that they plain suck, but obviously that's a matter of opinion as, somehow, they're still in business.

Anyway. The Daily Mash is a parody site, much like The Onion here on this side of the pond, but sometimes I learn more about British culture from them than I do from the BBC.

9 Like • Comment • View 4 comments

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