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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

November 5, 2019 at 12:01am

#969015

Suite Emotions

PROMPT November 5th

Write your entry today inspired by one of the emotions listed on the webpage below:

https://soulspottv.com/15-words-youve-never-heard-describe-emotions-we-all-feel-...

Just one? Damn. Usually I'd snark on most of them.

2. Liberosis:

(n) The desire to care less about things.

To loosen your grip on your life, to stop glancing behind you every few steps, afraid that someone will snatch it from you before you reach the end zone—rather to hold your life loosely and playfully, like a volleyball, keeping it in the air, with only quick fleeting interventions, bouncing freely in the hands of trusted friends, always in play.

I've been working toward this for most of my life. I mean, not the playful volleyball metaphor - I hate sports - but caring gets you nowhere, so I actively try not to. You know how pedants are always like "It's not 'I could care less' but 'I couldn't care less,' because 'I could care less' means you do care somewhat?" (Okay, I'm one of those pedants.) Well, I could care less. No, really, it is theoretically possible for me to care less. It's like one of those mathematical functions that approach but never quite reach zero and you're skipping this sentence, aren't you?

I actively try to care less.

It helps to know that no matter what we do, no matter what we as individuals or a species or the greater community of living things achieve, no matter how we spread into the universe, no matter to what heights of art, science, engineering, or something we currently have no word for we reach... regardless of any of that, the universe continues to race in the direction of higher entropy, and eventually, it will fade into oblivion. All of the energy transfer that could have taken place will have taken place, and every point in the universe will have reached an equilibrium, the same temperature. This is known as the "heat death of the universe," and "temperature" will have no meaning because there's no way to measure it, no one to measure it. Spacetime itself will cease to have any meaning. No process of life or anything else will be able to proceed, because any such process requires energy transfer, and I just said that that will wind down to nothing.

This is absolutely inevitable, and not only is there no way to stop it, but any attempt to do so will only hasten it because that's how entropy works. In fact, I've come to the realization that the purpose of life is to accelerate entropy, almost as if the Universe itself wants to end its own pointless existence.

In short, nothing matters and that's the big cosmic joke.

I'm aware that this sort of thing could cause an existential crisis for some people. At the very least, it can trigger the classic Five Stages of Grief, starting with denial. Deny all you want; that doesn't change the Second Law of Thermodynamics. But remember, the solution is to stop caring and laugh in the face of Fate.

In that vein, then, as per the linked article, I, too, can propose made-up words for emotions that don't really exist and it wouldn't matter if they did:

1. Zeppelinalgia

That feeling you get when you look to the west and your spirit is crying for leaving.

2. Grinchestia

The sadistic joy that can only be achieved through ruining someone's winter holiday.

3. Wonkanastia

The satisfaction of providing children with important life lessons by fitting their punishments to their misdeeds.

4. Johnwickitude

When someone wrongs you and you retaliate utterly disproportionately to the situation, and damn but it feels great.

5. Entropoeia

Per the above discussion, the moment of absolute darkness that envelops you when you realize that, in the end, nothing matters at all, followed by the relief you feel when snatch yourself back from the abyss in time to laugh about it. I mean, you did do that, right? Right? Hello?...

4 Like • Comment • View 5 comments

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