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 6 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 8 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').

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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.

May 16, 2021 at 12:04am

#1010240

For Better or Worse

PROMPT May 16th

What do you do to make the world a better place?

What, my mere existence isn't enough?

Seriously, though, I'm no judge of that. "Better" is a subjective quality. Sometimes what's good for one person or group is worse for another. We can't always know the full ramifications of our words or actions. As with the classic butterfly effect

in chaos theory, sometimes something small and insignificant can have huge consequences down the line.

Most times, though, the effects tend to dampen out and the end result is indistinguishable from random noise.

So, I don't know. I mean, I don't actively try to make the world a worse place. But when I think of anything I do to proactively improve things, I find my brain skittering away from the mere possibility of mentioning them. I would prefer not to shout virtue to the world. In fact, I take great pains to project an image of a selfish drunk who's only in it for himself.

Not that I haven't touted my own good deeds in the past, sometimes even in here. But I just never feel right about it afterward.

I guess I just feel like I'm often annoyed by the people who are like "Look at me! I give money to poor people! I help old ladies across the street! I only eat hyperlocal, organic, cruelty-free food! I'm so virtuous I make demons gnash their teeth in frustration and angels weep in jealousy!" And I don't ever want to be one of those people. Everyone has vices and virtues, and to proclaim one's virtues can make other people think you're hiding something horrid.

There are none so evil as those who claim to be virtuous.

There's another thing, too. Like, a lot of people, when they need to reference someone who is a Good Person™, they invoke the name of Mother Teresa. Mother Teresa was objectively a horrible person

who promoted the idea that Suffering Is A Good Thing, and the more you suffer, the closer you are to God. I have a word for people who promote suffering, and that word is: evil. No, she was a villain with a vast, powerful PR team. And yet a lot of people still think she made the world a better place.

So I prefer to keep such things to myself. People will spin anything I say or do the way they want to, anyway, and I'm not going to sit here and justify myself to others.

8 Like • Comment • View 6 comments

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