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 3 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.

September 12, 2020 at 12:13am

#993134

Drinking about Thinking

Today's prompt is kinda what journaling is supposed to be all about, right?

PROMPT September 12th

Write about something you need to get off your chest. What’s pressing on your mind?

Other than the bloody obvious, stare-in-your-mask-wearing-face bullshit that's consumed us all since somewhere around the beginning of the year, I'm drawing blanks.

I guess that's a good thing. Life, for me, could be -- and inevitably, at some point, will be -- so much worse.

Don't you just love realism? Oh, sure, some may call it pessimism, but I know better.

Yes, I miss being able to travel, but I'm pretty sure that's going to happen at some point (provided, of course, the aforementioned turn for the worse delays itself for just another year or two).

What I miss even more is being able to sit at a bar.

I don't mean just being able to go to a place that sells drinks, sit at a socially-distanced table, and have a few. I've had opportunity to do that. I mean sitting on one of a row of barstools, contemplating the neat lines of fine beverages behind the bartender, and slowly consuming one of them.

Fun fact: Virginia doesn't have bars.

I mean, sure, there are places like what I've just described, but thanks to arcane Prohibition-era laws that have not changed, we have no establishments whose sole purpose is to provide a variety of adult beverages. What we have are:

Restaurants with a bar inside.

Craft breweries / cideries selling their own product exclusively.

Wineries also selling their own product.

State-run liquor stores (fermented beverages can be sold in supermarkets and convenience stores, but not distilled ones).

Of course, this doesn't stop me from going in to a restaurant and pretending it's a bar. They've got the barstools and the liquor lineup, which is more than I can say for Utah. Or... they did before the pandemic; right now, no one's letting anyone sit at a bar. They do try to push food on you, though; the law I mentioned before says something like at least half of an establishment's revenue must come from food service, or they lose their license.

Somehow, though, we get by. Things always change, and even in the past 20 years a lot of the more restrictive rules have been relaxed. Like, I can now order beer for delivery. This was mostly a pandemic-related innovation, and we'll see if it continues. I mean, one of the main purposes of liquor laws is ostensibly to discourage drunk driving, and what better way to do that than by delivering the product to one's own house?

That said, I'm not sure they really want to discourage drunk driving; it's too much of a revenue generator.

So, like I said, I get by. I'm really not looking forward to the colder weather, and not being able to sit outside to order drinks at a restaurant, but I'll muddle through somehow.

Mini-Contest Results!

Surprise! Everyone's a winner today. Because yesterday was my account anniversary, I'm handing out gifts in the form of Merit Badges to everyone who commented yesterday. I won't be making this a regular event, though; this was a special occasion. And it'll probably be at least two weeks before I do another Mini-Contest, to avoid having to deal with CR time restrictions. But I suspect I'll do another "normal" one towards the end of the month.

The following commenters will get their MBs later because I've given them one recently: ⭐Princette♥PengthuluWrites

, Apondia

, and WakeUpAndLive~doingNaNo'24

. Everyone else who commented yesterday will get theirs soon. Thanks for reading!

7 Like • Comment • View 10 comments

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