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 13 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 15 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 5, 2020 at 12:06am

#982788

News

Full disclosure: I'm on the last glass of a bottle of Gewurztraminer from a Virginia winery. I suppose you might think that since I can still spell Gewurztraminer, maybe I'm not really drunk. Well, then, you don't know me.

PROMPT May 5th

Find a local news story that makes you feel something. Share the story along with your opinion on it in your blog.

So.

I live in Charlottesville, VA. Most of you already know that; it's not like I've been trying to keep it a secret or anything.

A couple of years ago, my small (~40K, give or take, depending on whether UVA is in session) town made the international news for all the wrong reasons.

The reasons are wrong because in order to protest the removal of a certain traitor's statue from a local park -- and by "park" I mean a one-square-block piece of downtown -- the fascist nazi confederate KKK scum had to import a bunch of people from all over the country, because while there certainly are racists in my town just like there are anywhere, they're far from a majority.

The guy you've heard about? The one who killed a girl and injured a bunch of other people? He was from fucking Ohio. You know. Yankee territory. And he was tried locally, convicted, and, last I heard, sentenced to a long goddamned time in prison.

Anyway, like I said, I'm drunk, so I'm probably rambling, and I'm also probably getting closer to actually coming down on a particular political side, something I've always tried to avoid in this blog, but it's getting harder and harder to do so.

So to address today's prompt, I actively looked for a piece of local news, which I don't usually do, even though one of my closest and oldest friends is a local journalist.

https://www.nbc29.com/2020/05/04/charlottesville-election-officials-offering-sel...

Charlottesville election officials offering self-addressed stamp to encourage voting by mail

Both political parties are holding primaries on June 23 and the registration deadline is only weeks away, but election officials are already seeing activity that suggests the virus will not stop the vote.

At first, this news confused me, probably because of the Gewurztraminer. Before my state -- which, incidentally, has a goddamn medical doctor for a governor -- instituted a lockdown of sorts, I distinctly remember going to the actual voting poll location and voting in the Presidential primary. No. I'm not drunk enough to tell you who I voted for. Yet. Point is, I thought the primaries were done?

But no, these are the other election primaries. Okay. Fine. Moving on.

Why does this make me feel something?

Because I'm an American. And a Virginian.

The most basic, the most fundamental, the most important right that we have as Americans, is the idea that our opinion matters. And voting is the most immediate exercise of this right. And so, anything that helps people, of whatever political orientation, exercise this right, I consider to be a positive thing.

Other localities haven't done this. Other places have put restrictions on remote voting. They've effectively disenfranchised anyone who understands that going out in public and mingling with other people doesn't just affect an individual, but has repercussions that interfere with everyone else's right to personal autonomy.

And that's what it boils down to, in my opinion: it's not about your right to get a gods-be-damned haircut. It's about my right to stay alive because after you catch the covid at your barber, you might come in contact with me. You'd think that the people who are always screaming about "right to life" would understand this basic principle, but that turns out not to be the case.

Either way, though, they have just as much right to vote as I do, or any other citizen does. Again, that's basic. That's what we're supposed to be about: everyone gets one, and only one, vote. Even if an election goes against what I believe in, I want to be able to at least think, "Oh, well, it was a fair election."

I can't think that if there's obvious bias in who can and cannot vote.

Now, I'm not one of those who proclaim that if you don't vote, you don't get to bitch about the outcome. Nah. This is America. You get to bitch whether you voted or not. But for shit's sake, don't try to suppress the votes of others. That's unAmerican.

Sigh. I guess I can expect a lot of shit from the other side on this one. And I've been so careful to be neutral, up until now. But, whatever. You have the right to your opinion. And I have the right to ignore it.

Damn. Finished that last glass. Guess I'll open up another wottle of bine. It's not like there's a shortage.

7 Like • Comment • View 15 comments

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