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.

April 8, 2022 at 12:02am

#1030288

Out of Phrase

I'm not going to go over every one of these, don't worry.

Everyday sayings explained

First, though, a couple of disclaimers:

1. The linked article contains some artistic sideboob in a photo. Just so you're aware if you decide to open it at work and your work frowns upon such things.
2. I didn't verify any of these. Some of them seem off to me. If you use any of them at cocktail parties, you may face scorn.

Some sayings are now so commonplace, we’ll utter them with no idea of where they came from. But every phrase, saying or proverb starts somewhere, and thanks to the Phrase Finder, we’ve uncovered the (often disputed) authors, meanings and stories behind some of the most commonplace sayings.

Not included: "rule of thumb." I got screeched at one time for using that phrase, because the screecher was convinced that it came from an old law about the size of the stick a man was allowed to beat his wife with. That is not the origin of the phrase. But her mind was made up and she was impervious to facts. I walked away.

Also not found: the falsehood that the F-word came from "For Unlawful Carnal Knowledge." While that was a pretty good Van Halen album, it is not the origin of that word.

I note these because there's a lot of misinformation floating around about word and phrase origins (and don't get me started on "blue moon" or we'll be here all day -- just search that phrase in this blog, as I've flogged that dead horse to undeath). Which is why I'm not sure how many of these are accurate.

Like I said, I'm just going to pick a few to comment on.

Chow down

'Chow down' was first used by the U.S. military during WWII. 'Chow' is a Chinese breed of dog, that became a western slang term for food due to the Chinese's reputation for eating dog meat.

If this is true, wouldn't that make "chow down" kind of racist?

Hair of the dog that bit you

This term for a hangover cure is another medieval saying, originating from the belief that once bitten by a rabid dog, the victim would be cured by applying the same dog's hair to the wound.

This origin is probably correct, but I should point out that neither use of "hair of the dog" does jack shit.

Off the record

This American phrase was first attributed to President Franklin Roosevelt in 1932, who was recorded in The Daily Times-News saying "he was going to talk 'off the record', that it was mighty nice to be able to talk 'off the record' for a change and that he hoped to be able to talk 'off the record' often in the future."

So he's on the record saying he'd like to speak off the record? Whatever.

As happy as Larry

This saying has Australia and New Zealand origins, but who is 'Larry'?

Unlike the others in this list, I'd never heard this one. Perhaps it's unknown in the US. (This article is from the UK.)

Two peas in a pod

Referring to the fact that two peas in a pod are identical,this phrase dates from the 16th century...

Having shelled more than my share of peas when I was a kid, I can tell you that not all the peas in a pod are alike. I suspect the phrase persists more for the alliteration.

Fly by the seat of your pants

This aviation term emerged in 1938 in US newspapers, to describe pilot Douglas Corrigan’s (slightly perilous) flight from the USA to Ireland.

Look, you're leaving out the best parts of that story. He was called "Wrong-Way Corrigan" for a reason.

Green-eyed monster

Shakespeare coined this term in The Merchant of Venice, when Portia says: "And shuddering fear, and green-eyed jealousy! O love, Be moderate;".

I've talked about this phrase before, in "The Play's the Thing"

-- another one about phrase origins. There, the claim was it originated in Othello. More importantly, though, it became the name of a drink I invented featuring absinthe and Midori. How was it, you ask? Hell if I remember. Absinthe makes the mind go wander.

Mad as a hatter

19th century Mercury used to be used in the making of hats. This was known to have affected the nervous systems of hatters, causing them to tremble and appear insane.

As far as I know, this one's truthful. What's not mentioned is that Carroll's Mad Hatter was based on the mercury poisoning thing, and not the other way around.

Now, some would say that such phrases as these are trite or cliché. Perhaps they are. But almost every cliché starts out as profound poetry.

Besides, knowing word and phrase origins is just fun.

I saw this on Sunday and I kept forgetting to do a review until just now. You'll see why.

One-Sentence Movie Review: Morbius:

With basically the same plot as pretty much every other comic-book character origin movie, though less well edited than most, this film is pretty forgettable except for the excellent special effects and the way Matt Smith rules as a villain.

Rating: 2.5/5

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