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:

Write_Mikey_Write!

about an hour 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

about 3 hours 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.

May 28, 2023 at 9:35am

#1050188

Revisited: "Poor You"

It's Sunday, so it's time to unearth an ancient fossil of a blog entry. This one's from early 2020 and references a Guardian article from half a year prior: "Poor You"

The article

I referenced is still there, so context is easy to find.

The article, and my commentary, are pretty much just as relevant now as they were three years ago (though one might be tempted to wonder how the somewhat sheltered author navigated the pandemic): wages aren't growing much, prices are, and people are still people.

So, a few of my comments that might warrant additional explanation:

1) I'm only giving her a pass on the "gluten-free cookbook author" gig because she is apparently diagnosed with celiac.

What I meant by this is that, for a while, "gluten-free" was a fad, and I detest fads. Nevertheless, there are people for whom it's not a choice, but a necessity, and if the fad gave them more choices for a reasonably healthy lifestyle, great.

2) $15 an hour? Stocking groceries? I'm not saying that's a lot of money, but it's above average for unskilled workers.

I have no idea if that's still true in 2023, but for the time, I believe that to be correct.

And yeah, being broke, or close to it, damages one's mind. The crappy cheap food you have to buy if you're poor doesn't help with that.

This probably wasn't the best way I could have phrased that. I wasn't trying to imply that poor people are brain-damaged. I meant it as an indictment of the system that forces some people to be poor, not to rag on the victims of that system.

Tying health insurance to employment is good for employers. Not great for people who'd rather spend their time running a small business.

By "good for employers," I meant that the incentive of keeping one's health insurance is another trick employers can use to trap you in a dead-end and/or low-paying job. The article's author, for example, apparently took the job mostly because it offered health insurance, rare for a part-time gig. People will put up with a lot of bullshit if the alternative is worse. This might have changed a bit in the last three years, judging by all the shitty employers whining "no one wants to work anymore." (In reality, no one wants to put up with your bullshit anymore.)

Now, workers have a bit more power in negotiation. I hope that continues, but it probably won't.

Veganism is a product of privilege.

I stand by this assertion. But I'm not presuming to tell people what to eat. You do you. My objections only start when it becomes like a religion, with self-righteous adherents and attempts at conversion.

I'm aware of the contradiction inherent in my attempt to convert proselytizers to the practice of minding their own business, but I can live with that.

In closing, sometimes "poor" is a matter of one's own perspective. One doesn't have to have a lot of money or a high salary to be privileged. Reading between the lines, this author had, at minimum, a place to sleep, an internet connection, and something to write and post with (laptop, smartphone, something). And some sort of support system. Not to mention the wherewithal to pursue her preferred diet, which requires a good bit of thought, energy, and time. This may have been a step down from her previous experience, but it's not rock-bottom, even if it seemed so to her. Truly poor people are rarely able to be picky about what they eat (which is why I call veganism a product of privilege).

Life has its ups and downs, and I sincerely hope she's doing better. And understands that she could be doing worse.

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