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 4 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 25, 2020 at 12:02am

#994138

Don't You Forget About Me

I find it unlikely that I'll be remembered much at all.

PROMPT September 25th

What specific character traits do you want to be remembered for?

If I am remembered, I'll have no say in the matter. What I want, therefore, is unimportant.

Hell, I'm not even sure what my character traits are. I'm too close to the matter.

When I was in high school, a guidance counselor accosted me after lunch one day. He said something like, "I just wanted to tell you, I was watching you at lunch. You were hanging out with the nerds, then you went over to the theater kids and talked to them. And then you talked to the jocks, the misfits, people in the band, and the minority kids. You seem to get along with everyone, all the different groups."

I hadn't really thought about it like that, and it didn't make a lot of sense to me, but after that, I noticed that yeah, not everyone could talk to just anyone. This was before The Breakfast Club came out, though, and after watching that movie, a few years after the guidance counselor incident, I think I finally understood, at least a little.

See, that movie never made a lot of sense to me, and I'm not just talking about how Ally Sheedy was fucking hot even before her supposed "transformation." It was that the movie made me realize that most people just hang out in their little cliques, but I never really had one, at least as far as I could tell. I just thought everyone was, you know... pretty much just a human.

Which is, of course, not to say that there weren't people I thought were assholes. Or that some people didn't think I was. It's just that I've always been willing to give anyone a chance, regardless of perceived social status or interests.

It's something, I think, that has served me well as a writer -- knowing people from different backgrounds has helped me with characterization and whatnot. But more importantly, it's helped me to put myself in another's shoes, whether those shoes were Reeboks (those were big in the 80s as I recall), sandals, dress shoes, or used footwear from Goodwill.

There is a downside to it, though, which is that I've never really fit in to any one group. The closest I come is when I'm in a brewery, surrounded by other beer drinkers. The next closest is at SF/Fantasy conventions, which I haven't been to in a while, but the people there tend to be accepting of differences anyway -- so long as you don't diss their favorite movies/TV shows/comics/books/whatever. But when you don't pick a "team," people are more wary of trusting you. After all, how do the science geeks know that you won't defect to the band nerds?

As an aside, everyone's a nerd. Everyone. We all have things we're passionate about, be it sports, music, politics, comics or whatever. Someone decided long ago that some interests have more value than others, and those with lesser-valued interests get branded as outcasts. Sports fans lost any right to look down on fantasy cosplayers, though, when they started painting their faces and wearing weird shit to watch their games. Everyone's a nerd about something.

So, if I were able to choose, I suppose that's what I'd want to be remembered for: accepting. It's certainly not absolute; there are some things I can never accept, like people who deliberately harm others, or who are blatantly racist. But if you're not hurting anyone, it doesn't matter to me. And my own interests are so varied that usually, I can find common ground.

Ask me again tomorrow and I'll probably say something else, but this is what came to mind today.

9 Like • Comment • View 8 comments

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