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!

4 minutes 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.

Adherennium Plotting something

about 2 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.

May 3, 2024 at 11:31am

#1070468

It's a Crime

I'll do another one from "JAFBG"

[XGC] today:

What issue do you think has been misrepresented?

Since I pick these at random, I didn't have an axe to grind in mind when I landed on this prompt. It took me a while to sift through all the issues I could remember from relatively recent news stories, eliminate from consideration those that are too divisive to deal with in the short time I take to write these things, and decide on one I gave enough of a shit about to comment on.

An AI could probably have done that faster, and indeed, I considered doing this entry on AI, perhaps even using AI (which is not actually AI, but that's a semantic bugaboo for me and a whole different level of misrepresentation).

Since I was in NYC last week, though, I decided on crime.

No, I don't mean I decided to pursue a life of crime. English is sometimes ambiguous like that, which can be annoying but can also lead to great amusement, so let's not change that anytime soon. What I mean is, I think crime is an issue that's been misrepresented in media, both social and commercial.

The reason I mention NYC above is that there's this pervasive attitude that "big city" crime is a huge problem, and in the US, there's no bigger city than New York. And yet, the reality is, though I can't be arsed to look up statistics, that most of NYC is pretty damn safe. Sure, crime happens... but it can happen anywhere, and if you're a victim of assault or mugging or whatever, the prior chance of you being a victim of assault or mugging or whatever is largely irrelevant.

Discussing this issue is made difficult by how one defines "crime" as well as other factors. Different localities have different priorities. In my experience, law enforcement makes a big show of drug busts, while mostly ignoring crimes with actual victims, such as burglary (yes, drug use is often a bellwether for other crimes, but that doesn't mean it is, by itself, worse than, say, sawing off someone's catalytic converter).

Mainly, though, the issue comes down to one of familiarity. As an analogy, most people in the US drive nearly every day, while they only fly occasionally. The dangers of flying are thus magnified in a person's mind, sometimes to the point of actual fear of getting on an airplane. Statistically, though, it's clear that you're much safer on a jet (even if it was recently made by Boeing) than you are driving to and from the airport. Likewise, someone from a medium-sized town like mine might be wary of the Big City with all its reported crime, while being used to the risks in one's hometown.

Similarly, when it comes to threats to your family, other family members (or former family members) are much more likely to be the problem than some stranger.

And then you get the politically-charged rhetoric about letting in immigrants and the like, who, according to the opponents thereof, are either lazy and want handouts, or are so willing to work hard that they're taking all our jobs; either way, though, they're perceived as potential criminals, which ignores all the US-born criminals who are much more likely to be the ones who do you some harm.

It's understandable to be concerned for one's safety. And it pays to take reasonable precautions. But listening to the media might give a person a warped view of where the actual threats to it are coming from.

3 Like • Comment • View 2 comments

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