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!

a day 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

a day 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.

July 28, 2019 at 12:28am

#963298

Trippin'

What does “vacation” mean to you? Alone time or time with friends and family? Staying close to home or traveling far afield? Spendy or thrifty?

When I had an office job, the only thing I usually wanted to do on vacation was spend time alone at home, to try to recover from work. I took the occasional trip, sure, but every time I did that, I needed a week to recover from the trip, and work is not the best place to do that.

Travel can be tiring. It took me a long time to finally decide what I wanted to get out of traveling - not days packed with activities, but a few activities and a lot of rest. Plus dining and drinking, of course; those are my primary purposes in travel.

As for location, doesn't really matter. The only distinction I make is between day trips and longer journeys. On the longer ones, I prefer to stay in hotels. After talking to other people, it seems I'm the only person who actually enjoys staying in hotel rooms. Well, most hotel rooms. I've had some stinkers - literally and metaphorically. To me, though, that's all part of the adventure.

And in case you missed it, I don't camp. Shudder. My idea of "roughing it" is staying in a three-star hotel.

Which brings me to the budget issue.

I believe in the idea that the best use of money is not stuff, but experiences. I don't lack for stuff, but I also don't go out of my way to collect it (well, except for shot glasses - I have a pretty good collection going). That's why a lot of my vacations are road trips. That's also why I've been known to blow money on first-class plane tickets, sometimes, when I'm not driving. You know the best thing about flying first-class? It's watching all the harried steerage passengers stumble past while I sit back in a generously-proportioned chair, with a gin and tonic in my hand.

It's glorious.

That said, I try not to go overboard on the expenses. I'm going to Vegas in a few weeks. Vegas can be expensive, especially if you gamble, but I scored almost-free lodging along with a "resort credit" promotion, which consists of a lot of free food and beverages - which, as I've noted, is the purpose of travel for me in the first place. I probably wouldn't be going if not for these perqs, at least not next month; August in southern Nevada can be... exhausting.

Before you ask, no, I'm not sticking around for the Area 51 joke. That's in September. I plan to be safely back on the other coast when (if) that happens. You can bet I'll be watching the news, though.

So yeah, when I travel, I do have a budget. It's just that my budget is usually fairly generous, because for me, travel is my main entertainment these days. Yes, that includes a gambling budget - I try to stretch that out over the time I'm there; it sucks to run out of money before I leave.

I've heard all the arguments against gambling, and I even agree with most of them. But to me, it's just another form of entertainment. I once saw a YouTube video of some guy who claimed to have spent over $20K on tickets to a major sporting event. That's his choice; it's not one I'd make, but to each their own, you know? Point is, my gambling budget isn't that high, and I can make it last longer than a few freezing hours in a stadium. Sure, the odds are stacked in favor of the casino - but is that not the case with most of the things we all spend money on? If the owner, or corporation, or whatever, wasn't making money, they wouldn't offer the event or product.

Next year, I plan on spending a good bit of money on a trip to Scotland. Even there, single-malt scotch is expensive, as is shipping the good stuff that they keep to themselves back to the US.

So that's a vacation for me - going somewhere, drinking, and basically enjoying whatever the place has to offer. When I get home, I'm still not doing anything productive, but at least for a while, I did nothing productive somewhere else.

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