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 2, 2020 at 12:02am

#994824

Dark and Stormy

I'm not firing on all cylinders right now. I think I've mentioned this before, but I've been fighting a toothache since approximately 15 seconds after my state instituted lockdown back in March, and it's only been about a month since the pain got so bad that I wanted the pain to go away even more than I wanted to, you know, not get sick -- and I can't think of many better places to get a certain airborne disease than at a dentist's office.

The other thing I've been doing is trying to get a flu shot. My pharmacy advertises them, but every time I've gone there in the past two weeks, they've been conveniently "out."

A root canal - actually, two of them at the same time - was scheduled for yesterday morning, and afterwards, as I went to pick up some prescriptions the endo had called in for me, behold, a flu shot was available. Now, I don't usually get major side effects from flu shots, but I think the combination of having someone dig around inside two teeth, the painkiller prescription for the aftermath, and the vaccine conspired to give me mental fog. It's a bit better now that I've had some rest, but I still don't feel all that coherent. A bit like being drunk, actually, only without the fun part of, you know... actually being drunk, or having drunk. (No, I didn't drink any booze and won't until the meds have run their course.) But I just can't seem to shake the fog right now.

Like, for example... as I've mentioned before, I've been working hard to learn French on Duolingo. The way that site is set up, lessons come in chunks of twenty exercises. Usually I get about 17-20 of the exercises right. I'm sure some people with better memories than mine do better, but hey, I'm slowly improving. Point is, when I went to do the lessons today I regularly flubbed five or six of the exercises for almost all the lessons. Stupid, basic stuff too, like using the entirely wrong word, making a wrong conjugation of a verb, switching genders (too tired to make a joke out of that right now), or typing "tu" instead of "te" when the pronoun is used as the object of a verb.

All of this is to say that I have a lot of things I want to do on WDC this month, and was hoping to hit the ground running; instead, I hit the bed sleeping.

Still blogging tonight, though -- I don't feel quite bad enough to break my streak -- and I expect things will get better once I've had some rest. And sorry if I flub English as badly as I did French earlier.

One of the things I wanted to do this month was a different blog challenge, besides the one I did yesterday, but I just don't have the concentration for it right now. So I'm falling back on my Blog Fodder folder. Here's a Cracked article about one of the most infamous fiction writers of all time.

https://www.cracked.com/article_27980_the-it-was-dark-stormy-night-author-had-su...

The 'It Was A Dark And Stormy Night' Author Had A Super Weird Life

"It was a dark and stormy night; the rain fell in torrents - except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness."

How Not To Write, Lesson One.

He also coined phrases that are still used unironically, like "the almighty dollar" and "the pen is mightier than the sword." But, more importantly for now, his life and its consequences were weird as hell.

Okay, those were things I did not know before reading the article. Of course, it's Cracked, so I can't be 100% sure that this is factually accurate, but now it's in my mind as "provisionally true" because in my current condition I can't be arsed to fact-check (though that's not much different from me on a good day). If someone else does that, feel free to comment.

Let's talk about his marriage first, because it'll make any relationship problems you're struggling with seem quaint.

I mean, I'm not going to paste the entire article here, because I don't want Cracked's crack team of lawyers slapping me with a plaig... plege... plegia... copying shit off their site lawsuit. But this stuff is seriously warped.

Now you know what they say about revenge: it's best served repeatedly and with increasing fervor over several decades.

Yes, I believe the Klingons came up with that proverb. In any case, that section deals with the very public spat between Bulwer-Lytton and his ex.

But of course it gets weirder.

But with the worst of their exchange over, Edward could get back to his writing, so now let's talk about the book that led to insane Nazi conspiracy theories.

Again, go to the link for details, but basically this guy, his memory now mostly reduced to a source of parody (I've done my own twists on the "dark and stormy night" thing), was popular and influential enough to affect freaking Nazi Germany a century later. And the echoes still reverberate today.

Bulwer-Lytton did not, of course, live to see any of that, but he did live to be offered the Greek throne.

I told you it got weirder.

Anyway, while that website varies widely in quality, sometimes you find a gem or two. And this particular one has to do with the lingering influence of the power of writing, so here I am, fighting off brain-cobwebs in an heroic effort to share the story with my fellow writers.

You're welcome.

Maybe tomorrow I can do something more coherent.

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