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 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 12 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 24, 2022 at 12:03am

#1032786

Sam: I Am

Just having a bit of fun today.

The Mysterious Jewish Roots of Yosemite Sam
Yo, Semites: Was the gunslinging, rabbit-hating Yosemite Sam Jewish all along? We spoke with the creator’s family to learn the truth

The article riffs on a certain former president's mispronunciation of Yosemite, but I'd be more interested in knowing if Porky Pig was Jewish. Yes, I know pigs ain't kosher. But as far as I know, Porky never ate pork, so... hm.

In one corner of Jew Twitter, Trump’s fuck-up also prompted an unexpected revelation about a 75-year-old cartoon character: Yosemite Sam. Yes, the belligerent, rabbit-hating, Bugs Bunny-antagonizing cowboy from Looney Tunes. Was he in fact… Jewish?

Twitter is nevertheless still a craphole.

"It being a strange world, Yosemite Sam is actually Jewish. He bore more than a passing resemblance to his creator, Isadore Freleng, and his full name is given in one episode as Samuel Rosenbaum."

Shouldn't be that strange. Jews are everywhere. There's probably one sneaking up behind you right now.

Later, by phone, Beck elaborated. “He’s a Western-bad-guy type. And we don’t associate Jews with that, I don’t think,” Beck says. “Bugs himself might have some Jewish tendencies, with Mel Blanc as his voice and a certain New York speech pattern.”

Oh? We doing stereotypes now?

According to Shaw, her father created Yosemite Sam in 1945 because he felt Bugs Bunny needed a stronger adversary than the dim-witted Elmer Fudd.

Dim-witted or not, he was brilliant in What's Opera Doc.

Freleng was also known to hide the occasional Jewish pun in his work, such as a 1954 cartoon titled Muzzle Tough (say it out loud).

The Warner Bros. cartoons had the best puns, period.

Speaking of, there’s the distinct possibility that Goofy is Jewish, having been developed by pro-labor Jewish cartoonist Art Babbitt, who helped lead a strike of lower-paid Disney workers.

Look, no. Warners: Jewish. Disney: Waspish. The Mouse and the Rabbit have battled since the dawn of time, and will be rivals until its end.

Anyway, in case it's not clear (sometimes I wonder these days), none of this is meant to be insulting to anyone or any group. These are cartoon characters we're talking about. Like I said, just a bit of fun.

4 Like • Comment • View 2 comments

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