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 3 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 5 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.

September 19, 2020 at 12:03am

#993687

Avalanche

I'm sure some things are worth fighting for.

PROMPT September 19th

Respond to this quote:

“Fight for the things that you care about, but do it in a way that will lead others to join you.” -Ruth Bader Ginsburg

I just don't know if I care about a goddamn thing enough to fight for it.

I'm sure I used to care. I have a vague memory about caring, and having that sucked out of me like dirt into a vacuum cleaner.

I mean, sure, there are things I like, such as music, booze, movies, science, reading, writing, games, my cats, a few people. Even some of those abstractions people love to talk about, but can't seem to define, like justice and freedom and all that rot.

But do I care enough to "fight?" What exactly does that mean? Protests? Petitions? Civil disobedience? Dueling pistols? Boxing? Wrestling?

Nah, sorry, can't be arsed. Best I can do is write.

But that's not the real problem, here. I'm sure that if I were in a better mood right now, I could come up with something I'd fight for. It's the other part of the quote that drives me to drink.

I don't have the slightest idea what "do it in a way that will lead others to join you" means.

All my life, I've heard the adage "one person can change the world." Well, that's demonstrably untrue. Sure, one person can kick a pebble down the mountain, but unless it hits other pebbles and loosens bigger rocks until half the mountain disappears in an avalanche, there's been no measurable change.

First, you have to climb that mountain, and, like I said... can't be arsed.

And I wouldn't want the responsibility of getting something started like that. I have a hard enough time convincing myself to do something; how much harder would it be if I tried to convince others? Especially since I'm hardly anyone's role model. And then people would have expectations of me, expectations that will chafe until I slink off and go my own way as I usually do.

Nope. Everyone has their own things they're good at, and this is most definitely not one of mine. Nor do I want it to be.

Let the people who still care do the fighting. At this point, I think it's a lost cause; we've been on a downhill slide since 1969, and it's only recently that this slide has accelerated. The pebbles are shifting, slamming into larger rocks, and before too much longer, it'll all come crashing down.

Me? I'm going to ride the biggest rock I can find just as long as I can, with a determined grin on my face and the hot wind in my hair.

Don't join me.

The avalanche has already started. It is too late for the pebbles to vote. - Ambassador Kosh

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