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 11 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 13 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 27, 2022 at 12:05am

#1032910

Under the Sea

I don't really have a lot to say in response to today's article. I just found it to be interesting, and the best-written piece I've ever read on what it's like to be a whatever; in this case, a Navy submarine sailor (so if you want to weigh in here, Sum1's Home

, feel free).

Nukes, Nubs And Coners: The Unique Social Hierarchy Aboard A Nuclear Submarine
Getting assigned to your first sub doesn’t make you a submariner and once you become one you’ll find yourself in a social structure unlike any other.

I would imagine that if you're working with a bunch of other people in exceedingly tight quarters, for months at a time, you'd need some traditions and customs in addition to the usual military codes of conduct. Hell, I can't be stuck with most people for more than a few hours at a stretch without having to retreat. Months? And to think I almost joined the Navy, albeit through the Academy.

A new crewmember is a Non-Useful Body, or NUB. He or she uses our limited supply of space, water, food, and oxygen. They are not welcome, but BUPERS (Bureau of Personnel) keeps sending them.

I get that any new people in the military get hazed and mocked. I even get why (there are a few reasons, not least of which is that if you can't take shit from your superiors, you certainly won't be able to take shit from the enemy). But it's one reason I never signed up. It'd be like:

Chief: "Waltz, I'd call you a tool, but that would be an insult to tools."
Me: "Yes, Chief. You're correct. I am utterly incompetent and always will be. I shouldn't even be here."

Or:

Chief: "Waltz, you're completely useless."
Me: *shrug* "Then why do you even want me to try?"

I think the psychology is meant to make the enlistee really very badly want to prove their NCO wrong. But I figure that would just be disrespectful; why not prove them right instead?

Anyway. Not much else to add to the article. Like I said, I just found it enlightening, as my primary source of information on what it would be like to be stuck with a bunch of people in an airtight vessel was Star Trek, and as much as I like Star Trek, I was never under any illusion that any of it was realistic, especially the wide corridors, spacious bridge, and ample recreational areas.

Incidentally, I once got curious to find out why the command center of a vessel is usually called a "bridge." Apparently it's a holdover from the riverboat days when the controls were on a deck that literally bridged the boat

, between the paddlewheels.

Or so I was told. It's entirely possible I was misinformed. After all, I'm useless.

Incidentally, if you want to mess with a sailor, call a ship a "boat," and call a boat a "ship." Want to know which is which? Don't ask me. But I very nearly picked up a Navy officer lady at a bar one time with that discussion. Until I remembered that I have a sworn rule against picking anyone up at a bar.

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