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 2 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 4 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.

August 29, 2022 at 12:01am

#1037049

Fly the Trendy Skies

I don't usually link to The Torygraph, but I am today.

The real reason why most plane seats are blue – and other curious facts about plane cabins

The answer to almost every "Why are..." question concerning airlines is either a) It makes or saves them money, or b) some regulation requires it.

From Ryanair and British Airways to American Airlines (the world’s largest carrier), airlines across the board incorporate various shades of blue in their cabin seats, and it’s no coincidence. There does appear to be some psychology behind it.

Because blue is associated with depression, which is one of the outcomes of suffering the indignities of 21st century air travel?

Blue is associated with the positive qualities of “trust, efficiency, serenity, coolness, reflection and calm,” according to Colour Affects, the London-based consultancy run by Angela Wright, author of The Beginner’s Guide to Colour Psychology.

Funny, those are also the qualities associated with [insert your zodiac sign here]. The astrology is probably more accurate.

Nigel Goode, lead aviation designer and co-founder at Priestman Goode, which has been delivering aircraft interiors for 30 years for airlines, including most recently the Airbus Airspace cabins, states: "Our job as designers is to reinforce the airline’s brand and make it more recognisable, but our primary concern is to deliver an interior that maximises comfort to create a pleasant environment.

Well, then, you failed.

“It’s all about making the travelling experience less stressful and blue is said to evoke a feeling of calm. While some of the more budget airlines might use brasher, bolder shades, most others go with muted tones. The overarching aim is to create a home-like relaxing feel, so airlines tend to use muted colours that feel domestic, natural and earthy for that reason."

How is blue "domestic, natural and earthy?" Also, if you want to make "the traveling experience less stressful," there are less questionable ways to do it like, oh, I don't know, not packing people in like olives in a jar?

Cabin lighting is also geared towards creating a stress-free atmosphere on board, particularly in newer planes which have introduced soft LED lighting to replace the harsher light used in earlier models.

Right. LEDs not having to be replaced nearly as often, and requiring less power, has nothing to do with it.

As a general rule, most long-haul carriers won’t install leather seating because they can get unpleasantly sweaty.

Fixing this for you: because leather's more expensive.

Synthetic fabrics breathe, which makes for a more comfortable experience.

They also absorb the farts of the last slob who sat in your seat.

In fairness, I've sat in leather (I think it was faux-leather but whatever) seats on an airplane before, and the problem isn't sweat, but less friction.

“Lighter-coloured interiors, however, are more commonly found in first and business class seats, given not as many people fly in those cabins as they do in economy, where you’ll see more of the darker shades," Mr Goode explains.

That explanation makes no sense at all. There's a fixed number of each on an airplane, and these days, they're all filled. I'm betting it enforces class distinctions.

Found only on wide-body aircraft like Boeing’s Dreamliner, there is a small room hidden behind what looks like a small cupboard from the exterior.

Known as the 'crew rest', this tiny compartment opens up to a steep staircase that leads down to a few seats and bunk beds where crew members can sleep.

Et alors?

There are large areas on wide-body aircraft that are not used in the lower level, which have not been converted into seating areas because of the low height and lack of windows - both of which make the space too claustrophobic for passengers.

Quoi? That's never stopped them before.

Passenger seats with dummies strapped to them are put through the 16G test, a process which involves hurtling the seat down a 'sledge' ramp at high speeds to simulate a plane crash setting. All seats are required to withstand a 16g dynamic force.

Right, because people can withstand a 16g force.

I'm going to let the "dummies" thing slide. I'm feeling magnanimous.

Seats on many low-cost carriers like Ryanair don’t have a recline mechanism, which also adds to the weight, and others go as far as removing the seatback net for magazines to help reduce weight.

Want to start an argument online and sick of talking about Chicago "pizza?" Assert that a passenger in a reclining seat has every right to use said reclining mechanism to its fullest extent.

They do, incidentally.

“There’s a big push at the moment for the magazine pouch to be relocated just a tiny bit higher to allow just a little bit more space," notes Mr Goode.

Wow.

As an aside, for a while there, at least one airline (I think it was American) forbade passengers from sticking anything into the pouch other than the stuff that's native to it (safety card, barf bag, overpriced consumer goods ads). This was likely the most idiotic change to airplane rules since the non-smoking section (kind of like a non-pissing section in a pool, and I say that as a cigar smoker). Last time I flew that airline, though, there was no mention of this.

Anyway, snark aside, some of this stuff is interesting, whether you fly or not. Me? I used to love flying, but these days, it's nothing but a hassle. I might change my mind, though, if they relocate the magazine pouch just a tiny bit higher.

5 Like • Comment • View 2 comments

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