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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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').

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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.

July 27, 2019 at 12:22am

#963255

TEDdy Bear

If you were to give a TED talk, what would it be about?

I'm not overly familiar with that format.

I've seen a few of them, occasionally, from time to time. But I don't even know what, if anything, TED stands for; why there's a TEDx also; what the purpose of them (as opposed to other kinds of lectures) are; or why it gets a special name. I could look all of these things up, of course, but... can't be arsed.

However, the ones I have seen, as I recall, have been from credentialed experts. The only credential I have is a BS degree (take that as you see fit), and I'm an expert in nothing except maybe procrastination.

To play along with the blog prompt, though, let's assume I can get credentials and gain a few levels in knowledge about something. What would that something be?

Saying "writing" would be cheating, so let's not go there.

I am of the considered opinion that "self-help" speakers are good at helping themselves first, with any benefit to their audience being incidental. While part of me would like to get in on that sweet gravy train, I could no more do that than I could become a preacher. Damn conscience. So that's out.

There's an argument that I trot out once in a blue moon that explains why the popular definition of "blue moon" is an error, and it actually means something else. I don't know why this bugs me as much as it does, but it does bug me. I know part of the reason; it's because it illustrates how stubbornly people cling to false beliefs even after being presented with evidence that they are wrong. If I could choose one topic to lecture on, it would be that. I'm not going to rehash the argument here; if you're interested, here's a seven-year-old blog post on the subject.

Not sure it's worthy of a TED talk, though.

So, in the interest of just picking something and getting it over with already, I'm going to go with the "common misconception" theme and say: "If Humans Evolved From Apes, Why Are There Still Apes? And Other Misinformed Questions About Evolution."

Probably should give it a shorter title, though.

Ask me again tomorrow, or next week, or next month, and I'll have a different answer.

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