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 1, 2020 at 12:17am

#984737

Monster

I thought I'd go ahead and kick off the month of June with an entry for "Journalistic Intentions"

[18+]

A bit of background if you can't be arsed to click on the above link: Long ago, Turkey DrumStik

created a quote-remixing In&Out, which can be found here: "Fill in the Blank"

[18+]. Go ahead, give it a try; it's fun. The idea is to change a tired old clichéd sentence into something new, which is definitely an idea I can get behind. So for the June round of the blogging activity, she's selected fourteen altered clichés to choose from, submitted by our fellow members.

One of them was my own, so the least I can do is participate in the blog activity. So eight of my entries for the next five weeks will be inspired by these quotations. As usual, I'll be picking these at random as a personal challenge to see if I can come up with something interesting from anything, which has always been a kind of point of pride with me.

1. An over sized, monster truck on the highway with a competition sound system may not solve all your problems, but it will annoy enough people to make it worth the effort.
(Winheim Witheiw

)

You know, that sort of thing does annoy me, I'll admit it. But mostly just because anything loud that is not music annoys me. Dogs barking. Lawnmowers. Harleys. Leaf blowers. The trash truck on Tuesdays. Porn videos. But music is usually fine. Hell, if you're tooling down the road with your speakers cranked up to 11, and if I can hear the music over the blast of the face-melting sound system in my own Subaru, I might even like it.

Not so much the exhaust system.

But you know, I find there are two types of people in the world: people who think that there are two types of people in the world; and those of us who know better. Okay, no, seriously, there are at least two common reactions to the monster-truck-loud-on-the-highway scenario:

1. Meh, whatever. You do you.
2. There oughta be a law.

These two reactions typify pretty much everything. Someone's smoking a cigarette on their lawn. Someone's chewing their gum too loudly. Someone fails to put the shopping cart into the parking lot corral. Well, okay, I lean authoritarian on that last one. I mean, really, how fucking hard is it? I don't care if you have brats or you're in a hurry or both. You should have planned better. In both cases.

But if something isn't doing actual, immediate harm, I generally let it go. There's plenty enough drama in the world without adding to it by getting all complainey. So yeah, I lean toward #1 above. I know my rights, and one of them is most definitely not the right not to be annoyed.

I will say this, though, if you're one of the monster-truck-loud-stereo types, at least assuming you're a guy (which is a fair assumption if you're driving a loud monster truck):

I'm very sorry your penis is so small.

4 Like • Comment • View 2 comments

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