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!

a day 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

a day 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 6, 2019 at 1:04am

#965674

Last Words

PROMPT September 6th

I have long adored the practice on WDC of memorializing the portfolios of members who have passed away so all their writings remain visible without needing a membership. See: "White Case Memorial"

and "Request a Deceased Member Be Memorialized"

Do you hope to be remembered for your writing? What do you think your writings will say about you when you’re gone? Is your WDC portfolio in suitable shape to be memorialized tomorrow if you were no longer around to tend it?

A while back, I changed my handle to something unutterably silly for a time. I don't even remember what it was - let's say it was Fluffy Bunnykins. So there I was, Fluffy Bunnykins, when it hit me: what if I die tonight? And then my portfolio gets memorialized forever as Fluffy Bunnykins. Not that I ever expect to be taken seriously, but that would just add insult to the injury of my croaking. I made sure to tell my friends to have someone change my handle back to Robert Waltz if that happened. Knowing my friends, though, they'd probably change it to Dead Bunny.

It's the unavoidable reality of life that any of us could die at any time, with or without warning. Rogue seagull invasion. Falling piano. Too much sex. Quantum fluctuation. Whatever. We all know this, at some level, though most of us would rather die at 99, drunk and surrounded by hot sexy scantily-clad women wailing at the terrible loss. Or, I don't know, is that just me? Point being, while we know this, it's probably unhealthy to obsess about it. That's why comedy exists - to take our minds off that sort of thing. Because this might be the last sentence I ever write. Or this one. Or maybe this one. No? Okay, cool.

That said, there's not a whole lot in my life that's in good shape for my inevitable demise. Whenever I think about that sort of thing, though, I become aware not only of my own mortality, but of the sheer amount of work involved in preparing for it: finding a godparent for my cats; cleaning my room; making sure the stove's off; securing my porn from accidental discovery; keeping my vast fortune out of the hands of my ex-wife; making my WDC portfolio easier to navigate; arranging for a good home for my liquor collection... the list seems endless. And then I break out in hives, because I'm allergic to work.

On one hand, I won't care, because "I" won't be around to care. On the other hand, I'm creating work for other people, and that seems wrong.

Some years ago, as I recall, someone on this site died suddenly. Morbidly curious, I checked out their blog. Their final entry ended with "Life seems good." To my shame, I can't remember their name - I don't think they were ever whitecased - but I don't think I can ever forget those particular "last words."

With my luck, mine will be something like "See you tomorrow!" Only with a typo. Because I hate when I make typos, so that's precisely what I don't want to be remembered for.

See you tommorrow!

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