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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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').

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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

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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

July 3, 2023 at 2:36am

#1052054

Another Fine Mess

Finally, some vindication.

What If You Just Didn’t Clean That Up?

Good news: America has officially entered its messy-house era.

Like I needed to wait for permission.

Then, this past week, Marie Kondo herself admitted her house is a mess now that she has kids, a statement that was received like a divine pardon by mothers the world over.

I guess the mess finally sparked joy.

I’ve been waiting for this change for a long time, not because I love a mess, but because I have always had conflicted feelings about the moral supremacy of cleanliness.

I want to make a distinction here that the article kind of glosses over, at least at first: there's a difference between mess and clutter. Mess, to me, is not cleaning up your cat's puke, having pizza boxes lying around, or leaving dirty dishes in the sink. There are reasons to deal with messes that have nothing to do with morality, such as minimizing bug infestations. Clutter, on the other hand, is just stuff being organized in non-traditional ways.

The problem comes in when the clutter gets in the way of cleaning up the mess.

...mess is a sign of minds engaged in more important pursuits than tidying up.

And that used to be my excuse.

We need our ideas about cleanliness to catch up with reality, because they are stuck in the mid-20th century, when most women didn’t work outside the home.

We also need to stop using staged real-estate ads as an ideal.

Women were responsible for housekeeping for thousands of years, up until just a few decades ago.

[citation needed]

For two-income families who can’t afford a full-time housekeeper, maybe caring less is where the solution lies.

There is, indeed, a great deal of freedom when you finally stop giving a shit.

I know there are some readers who bristle at this because it smacks of lowering one’s standards to accommodate masculine laziness.

The messiest people I have ever known, not excluding myself, were my first wife, and a woman I dated for a while in the 90s. I freely admit that I'm lazy, but compared to them, I'm a cleanaholic.

Valid point!

No, it's not, you sexist sow. The neatest person I know was a guy who lived in my spare room for a couple of years.

Cleanliness has historically been about well-being, peace, and, to a lesser extent, health. But “clean” and “dirty” are also categories dreamed up by social groups.

I'll also point out that there's an element of privilege involved.

My parents came of age during the Great Depression. That period, at least in the US, left scars on the people who lived through it. They hated to throw anything away, on the grounds that it might come in handy one day. It's a scarcity mindset. If you keep throwing your stuff out, then you have to keep buying more stuff to replace it later on. This only helps merchants, and I'm pretty sure that's why they keep promoting minimalism: it's basically a marketing ploy.

Best to not buy all that shit in the first place, but obviously, the marketers don't go in that direction.

Meanwhile, product marketing has convinced us that we have to clean obsessively for our health. I can report from extensive first-hand experience that things can get quite filthy before people are actually getting sick.

And that's the other marketing push: buy these cleaning products to improve your life!

In conclusion, while I have some issues with the way the article is presented (not just the stereotyped gender roles, but way too many mentions of DikDok), I appreciate that someone else understands the value of not living in a perfectly curated space. It's one less thing to be neurotic about in a society that tries to make us neurotic about everything.

5 Like • Comment • View 5 comments

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