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 8 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 10 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.

July 20, 2020 at 12:01am

#988635

Man on the Moon

“If they can put a man on the moon, why can’t they put all of them there?”

PROMPT July 20th

In 1969, Neil Armstrong first set foot on the moon. Afterward, people commonly complained, “If they can put a man on the moon, why can’t they ______.” How would you finish that statement today?

make moon landing hoax conspiracy "theories" go away.

Seriously, this is the stupidest damn thing since flat-earth bullshit.

This nonsense pisses me off more than other nonsense, though. And I'll try to put the reason why into words, but I'm not sure I'll be successful.

There has always been an undercurrent of willful ignorance in humanity in general and the US in particular. I think people want absolutes, but there's no such thing, so there's backlash. "What do we really know, anyway? How dare we try to find the answers when we're merely human?" That sort of epistemological bullshit.

The Apollo program, political though it was, and born out of the worst case of national dick-measuring to ever consume two countries, was one of the greatest achievements of humankind. Taking a cue from the concentrated effort we made in World War II to construct nuclear weapons, we used the same sort of scientific/technological think-tank approach, not for the purpose of blowing people up (though that was always a hazard with the kind of propellants they used), but for a peaceful project.

And there's no doubt that it happened. I mean, we can be as certain about it as we can be about anything.

Hell, faking it in 1969 would have cost even more money than the actual moon landing did, and you'd have to somehow convince thousands of people to keep the cover-up a secret. People who worked on the project. People who covered it for the news. People who watched the launches. The astronauts themselves.

And yet... I suppose some of these know-nothings just can't wrap their heads around the idea that humankind can actually achieve anything. I really can't think of much else that would motivate the deniers, apart from an abiding contempt for themselves and their fellow humans. It's the same sort of mindset that makes them believe that we couldn't possibly have built the pyramids or Stonehenge or whatever, so it must have been aliens.

"I'm stupid and I couldn't have done it; therefore, no one else could have either."

I guess. I don't know.

To deny the achievement of landing dudes on the moon is to deny the fundamental potential of humanity itself.

So really, very little pisses me off more than this sort of thing. I'm not advocating suppression of freedom of speech, but such bullshit has to be met with reality, facts, and, yes, utter scorn.

I'm also not advocating punching the idiots who spout that crap.

But I don't blame Buzz Aldrin one bit for doing so.

8 Like • Comment • View 11 comments

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