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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 22 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 24 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.

January 22, 2020 at 12:03am

#973927

Running On Empty

PROMPT January 22nd

Your bags are packed. You have unlimited funds and resources to travel anywhere you want. Where do you go, who do you bring with you, and why?

Thanks, yeah, remind me about how I'm not going to get to go to Scotland with my friend.

There's a part of me that wants to travel, and keep traveling, and never look back. It urges me to go out there, anywhere, everywhere, see all the sights, do all the things, drink all the booze, while I still can.

For what? Asks the other part of me, the part that wants to stay home and run a routine. What's the point? It's not like you have anywhere to run to, or anything to run from. It's comfortable here. And besides, you have cats counting on you. All those travel experiences, sooner or later, all those moments will be lost in time...

So, as with anything else in life, we compromise. I stay home most of the time, but sometimes I go out there, looking out at the road rushing under my wheels. Other times, I fly, even if, sadly, not under my own power.

A few entries ago, I wrote, "There are few people I can get along with for more than a few hours or days." It occurred to me much later that this could be interpreted in at least two ways. What I meant by it was that I don't like to inflict my presence on other people for very long. So, I generally travel alone. I don't have to, though. I'd bring anyone who can put up with me.

As for where? Well, where not would be a more appropriate question. I'd probably stay out of war zones. And there's no point in going where there's no booze. Plus, my idea of "roughing it" is staying in a two-star hotel; camping in the wilderness is a hard pass. So is trekking across Antarctica. Fuck that noise.

That still leaves a lot of ground to cover. And ocean; cruise ships count as "not roughing it."

Some things on my wish list: Trekking across Canada the way I've done with the US - summer only, thanks. The civilized part of Alaska; also summer. Japan, for many reasons, chief among them a particular brand of Japanese whiskey I just can't get in my country. A river cruise down (or up; I don't care) the Danube. A few weeks in France, sampling as much wine as I can. Belgium, for the beer and the food. Germany. Scotland, as I've noted (technically, I've been there, but didn't get to drink any scotch). The Caribbean. Parts of Central America (see above about staying out of war zones). Parts of South America; that is, the parts that don't involve piranha nibbling on my tenders. Australia, New Zealand, Iceland. There are other places, but that's a start. Hell, I'd even consider Antarctica if I can mostly stay on the cruise ship.

And so we come to "why." I'm trying to resist the temptation to leave it at "why not?" Why does anyone do anything, knowing full well that there's only one certain destination, after which everything else you've done won't matter anymore? Well, if nothing else, it'll give me more stuff to write about.

Isn't that enough?

If it takes all night, that'll be all right
If I can get you to smile before I leave
Looking out at the road rushing under my wheels
I don't know how to tell you all just how crazy this life feels
Look around for the friends that I used to turn to to pull me through
Looking into their eyes, I see them running too

Running on (running on empty)
Running on (running blind)
Running on (running into the sun)
But I'm running behind

Honey, you really tempt me
You know the way you look so kind
I'd love to stick around, but I'm running behind
(Running on) You know I don't even know what I'm hoping to find
(Running blind) Running into the sun, but I'm running behind

7 Like • Comment • View 6 comments

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