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!

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 15, 2019 at 12:20am

#969731

Now, Where Was I?

PROMPT November 15th

In your entry today, write about focus. Use the following questions to guide you. At what time of day are you the most focused? When you need to focus on a task, how do you prevent distractions? How do you manipulate your environment to keep yourself focused? How else do you practice focus in your life? Any tools or techniques you can share?

Let's see if I can focus long enough to respond to this...

Nope. Just checked my phone. Had texts. Responded to them. Now, where was I?

Oh, yeah. Focus.

You may be wondering why I didn't know I had texts. That's because I have to keep the sound off on my phone during the week. I get up to 20-30 calls a day (no I am not exaggerating) from "health insurance" robocall scams, and if I don't keep the sound off, that's all I hear, all day: my phone going off. It's not so bad around midnight when I'm writing these entries, but if I turn the sound on in the evening and forget to turn it back off, then the fucking things wake me up in the morning and I get grumpy for the entire day.

No, I can't block them. I've tried, but they spoof numbers and it's worse than playing whack-a-mole.

What's more, when I'm trying to actually DO something on the damn phone, like compose an email or text someone or simply take notes, I'm often interrupted when the incoming call screen silently pops up. And then I have to wait. I have to wait, because if I hit the Reject button, I think they'll know that someone actually interacted with the other end and they'll call even more. This makes me grumpy, too, because only I am allowed to interrupt myself, which I do a lot, because I can't focus.

So why don't I change my number? No. I've had this number for 20 years and I'm not going to change it. I shouldn't have to. That shit simply needs to stop. Besides, they'd just start calling the new number.

Lately the calls have been in Spanish and Chinese (presumably Mandarin, but I can't distinguish between dialects of Chinese). I guess they figure that since I'm not responding to English, they'd try the other two major world languages.

I'm waiting for them to try French. Then at least I can use my newfound skills. Now if they want to impress me, they'd call in Klingon. Not that I've spent any time studying Klingon, but the language is unmistakable. If a Klingon offered to sell me health insurance, well, that'd be an offer I'd have difficulty refusing. Fortunately, I'm all out of latinum.

Hey, I wonder why with all the proliferation of various cryptocurrencies out there, how come none of them are called latinum (after the fictional medium of commerce of the Star Trek universe, if you're unfamiliar)?

Oh. I should have known.

But I'm meant to be talking about focus, aren't I?

Anyway, I've given up on focus, I've given up on trying to prevent distractions, and I arrange my life around knowing that I'm going to get squirrelled on a frequent but irregular basis.

Really, it's a miracle I get anything done at all.

5 Like • Comment • View 8 comments

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