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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Write_Mikey_Write!

about 5 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 7 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').

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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 24, 2024 at 1:02am

#1069547

Tipped Out

Yes, the article I'm sharing today was one of my inspirations for the Comedy newsletter editorial that just came out: "Keep the Tip"

. It's coincidence that my random number generator picked it out of my queue today.

What is the new etiquette for tipping?

I've also done other blog entries on the subject before, but this is a relatively new take, from NPR.

Businesses that never seemed to ask for a tip before — like grocery stores, self-checkout machines and fast food restaurants — are now asking for one these days.

As I noted in the editorial, I can't personally confirm the self-checkout tip chutzpah, but this is not the only source that asserts that it's happening. It's rare to find begging that blatant and uncalled-for.

If a business you don't expect to ask for a tip is suddenly asking you for a tip, what should you do?

Ideally, take your business elsewhere.

But Shubhranshu Singh, a marketing professor at Johns Hopkins University, likes to leave a 10% tip. If an establishment is asking for a tip, it's often an indication that the workers there are not getting paid a minimum wage.

If the workers aren't getting paid a minimum wage (outside exempt employees such as restaurant servers, who are some of the few that should be tipped), that business needs to face consequences for it. How that would work, though, I don't really know.

Some businesses load their payment systems with default minimum tip options of more than 20%. If you don't want to give that much, don't worry about holding up the line to take an extra moment to select the "custom tip" option, says Singh.

In those situations, I select the "no tip" option, and definitely try to find somewhere else to shop in the future. I know it's usually not the workers' responsibility to set those defaults. Still, it's bloody outrageous.

Don't forget to tip people who you might not have a direct interaction with, like hotel housekeepers, says Singh.

I'm torn on the whole tipping hotel housekeepers thing, honestly. I've done it. I've skipped out on doing it. I feel like it should be done for extended stays, on the theory that a tipped housekeeper might go the extra mile for you and hopefully not put itching powder in your undies. This makes it more of a bribe than a tip.

Tipping is also a way to pay workers more without actually raising their wages. It allows restaurants to get more money to workers while still keeping their prices low, says Sean Jung, a professor at Boston University's School of Hospitality Administration.

But if tips are expected and customary, as with restaurants, the "low" prices (they've still gone up along with everything else recently) are a lie. Nevertheless, some restaurants have experimented with no-tip options. Usually, this means raising their prices by 20-25%. Then, when comparison shopping, a potential customer sees higher prices and balks, ignoring which places take tips and which don't. Every place I know that tried this route went out of business.

In other words, it needs to be across the board, which means either a) collusion, which, as I understand things, is illegal; or b) regulations, which are already overdone.

Tipping culture in the US is so ingrained that there's not much will to do either. And even if they did, people will still try to tip, because it's what they're used to doing.

Oh, well... at least this article, unlike some others on the topic that I've shared here, doesn't rehash the false TIPS backronym, which, as I've noted repeatedly, has been thoroughly debunked. And yet, the article is light on practical information and encourages way too much work for the consumer, who just wants a damn hamburger.

I'm not saying people shouldn't get decent pay. Quite the contrary. I'm just saying it shouldn't be laid directly on our shoulders. I'd prefer to see the actual price of things up front (and this also goes for hidden fees from businesses like airlines, ticket sellers, and hotels). Until that utopia comes into existence, though, I continue to tip waitstaff and bartenders.

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