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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Turkey DrumStik

about 5 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

December 7, 2018 at 12:03am

#946988

Cold Inside

Another year, another shitstorm about holiday songs.

https://www.bbc.com/news/entertainment-arts-46425160

Baby, It's Cold Outside is one of those Christmas songs that's about as traditional as mince pies.

But an American radio station's decision to pull it from playlists because it's seen as unsuitable in the #MeToo era has reignited a debate about the song, and raised questions about other potentially questionable Christmas classics.

First of all, let me state outright that my life would not be lessened in any way if I never heard another holiday song. It would, in fact, be improved. Ideally, I would never step into a store and be bombarded with "White Christmas" or "Santa Claus is Comin' To Town" or especially "I'll be Home for Christmas."

There are a few that I can tolerate, but for the most part, if I never had to hear another Christmas song, I'd be happy. Or at least a little less depressed, which for me amounts to the same thing.

Okay, now that that's out of the way, I'm going to talk about the controversial songs.

What a lot of people miss when consuming media - be it audio, video, or whatever - is historical context. The platitude about people who don't learn from history being doomed to repeat it holds true here.

Things were different in the past. That's why we call it the past. Lots of things that were created in the past couldn't be created today, not in the same way. Blazing Saddles comes to mind. That movie was a product of the 1970s just as sure as Watergate and disco were. Movies like that one were created to shine a spotlight on the stupid attitudes of the time, and played a role in eliminating them. Once these attitudes became obsolete, a lot of the context of the movie was lost. If you don't know what race relations were like in the 70s, you'll miss a lot of the subtext.

As writers, one of the greatest things we can hope for is that something that we write - be it a story or a song or whatever - helps to change things. In the process, often the writer's work becomes obsolete. People later will miss the point, unless they understand the historical context. It's a bit like doctors working to eradicate disease - once it's eradicated, people in the future will start to wonder what all the fuss was about. Hence you get some of the most egregious types of reactionary in the present, like anti-vaxxers. Lacking the historical context of polio outbreaks and measles epidemics, they just don't understand why people make a big deal out of vaccination.

The song in question - and make no mistake, I think it's just as crap as any other "holiday" song - was a product of its time, and a wish for things to be different. Well, now things are different. We're closer to social equality than ever before. We're open to different expressions of gender identity. Things that once were forbidden are now commonplace - and that's not a bad thing.

But if we forget where we came from, the road that took us to this place where we are, we risk going back to it. You can try to make this a generational thing - I'm going to save my rant about "generations" for another entry, as this one's going on long enough - but it's not so much about generations as it is about ignoring history. Yes, things were worse in many ways in the 40s. But to know exactly how they were different can only highlight how far we've come, and how far we still need to go.

And I think the bigger problem is that once-respected news organizations like the BBC are quoting Twatter. If anything needs to go away, it's not old Christmas songs; it's shallow social media.

Let's work on that one, shall we?

I'll wrap this up with one of the few holiday songs I can stand:

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