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.

December 31, 2021 at 12:03am

#1023884

Requiem for a Year

Well, that was a year.

I know I said yesterday that I'd do a recap or something, but I can't be arsed. Besides, there's not much about this year that I want to remember. Best thing about it is I got my eyes fixed. Yay me.

I'm not one for making New Year's resolutions. I used to, but I do try to learn things in life, like not to keep doing the same thing over and over and expect different results. My mother liked to chant, "If at first you don't succeed, try, try again." Which, now I think of it, is ironic for someone who tried over and over to have a child only to end up adopting one. One who ended up being a gigantic disappointment.

I'm also not a fan of social media in general, but there is one app that I use regularly. It's called Untappd, and it's a place to record what beers you've tried and rate them. I call it "social media for drunks." I kind of wish they also did wine, or at least that I could find a different one for that purpose. But my first love is beer, so whatever.

So I was looking in my Untappd records a few days ago, and discovered something distressing. In 2020, I checked in 648 times. In 2021, my number of check-ins was 520.

I can't go on like this. I mean, a 20% reduction? That's outrageous. So my goal for 2022 is to drink at least 650 beers. They don't have to be all new to me, but I want my numbers back up, dammit.

I know, I know, that sounds like a lot, average almost two beers a day, but remember, a good number of those were from tasting flights. As in, a lot of times, I just took a couple of sips of the brew. The only way, therefore, that I can get back to my 2020 numbers is to visit more breweries and get more tasting flights.

What with everything going on right now, whether that's possible or not is up in the air. But it's something to reach for, and everyone needs a hobby.

Speaking of hobbies...

One-Sentence Movie Review: The King's Man

A movie that reimagines the events leading up to and surrounding WWI and the Russian Revolution, the best thing about this movie was the character of Rasputin; other than that, it's pretty standard political/spy stuff that thinks it's more clever than it actually is, but also features several great fight scenes.

Rating: 3/5

And so ends 2021, and good riddance. Everyone have a happy New Year, and, at the risk of sounding clichéd, see you next year.

As it has become my habit to post one of these just after midnight, remember tomorrow's entry won't follow that pattern, as I will be in no shape to post then. But I'll get one in on New Year's day.

Sometime.

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