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!

about 11 hours 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 13 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.

June 5, 2020 at 12:01am

#985027

Oh Behave

Here's another entry for "Journalistic Intentions"

[18+].

2. Well-behaved women rarely do behave well, they just make everyone else think they do.
catty

I'm familiar with the original version of this. "Well behaved women seldom make history." Fair enough, I suppose, though I'd argue that well-behaved men seldom make history, either, making that a nonsequitur of sorts.

There's more than one way to make history, and just because you do doesn't mean you've done a good thing. Carrie Nation, for example. Certainly not well-behaved, and one of the most evil people who ever existed.

But this isn't about the original quote; it's about the remix.

We all have our rebellions. Nobody does everything expected of them, all the time. Not only is that impossible, but if you told me you never even once rebelled as a teenager, you're either lying or boring. Hell, most of us make it a point of pride. "I was supposed to go to work today, but I called in sick. Yeah, sick of work." The important thing in a situation like that one is to not brag about it on social media.

In fact, so many people have been busted for doing something naughty because they posted about it on social media that I have had to once again lower my opinion of humans' collective average IQ.

Of course, there's misbehavior and then there's outright fraud. I have no sympathy for someone who claims disability for a bad back and then posts pictures of themselves climbing a mountain in their copious free time, and thence gets their benefits cut off. But stuff that's not really hurting anyone? Eh, you do you, or whatever the saying is these days.

So if I ever see someone, of any gender, who presents themselves as a fine, upstanding member of society, always doing the Right Thing, signalling the fuck out of their virtue, well, I don't buy it. Oh, I'm sure that, like I said, there's a preponderance of good people in the world, but also like I said, sometimes good people do naughty things. If you're vegan, I assume you sneak a bite of cheese every now and then. If you're always talking about recycling, I bet that sometimes you get in a hurry and throw an aluminum can into the landfill trash. It's okay. I don't think less of you for it. I don't even think less of you for lying about it, because really, you're not hurting anyone and a little bit of rebellion can feel so damn good.

But if you're a fiery anti-sex preacher and you get caught having an affair? Then I'm going to laugh. Or you pull a Carrie Nation and rail about the evils of alcohol, and I find you getting wasted in a bar 100 miles from home? You're damn right I'm going to take pictures and spread them around.

We're all hypocrites to some degree; no one can be perfectly consistent, especially over time and growth. But if you're going to be that blatant about it, you will definitely get called out.

And no, I'm not going to take the gender bait. Not this time, anyway. I reserve the right to be hypocritical about that in the future.

3 Like • Comment • View 2 comments

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