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.

August 16, 2021 at 12:03am

#1015683

Error Prone

Today's thing is mostly a collection of images, and since I can't be arsed to retype things, I won't have much commentary.

30 Phrases Many People Don’t Know They’re Using Incorrectly

I know I'm not immune to making errors, and I suspect that no one else is, either. If you think you are, then that in itself is an error, which leads to paradox.

No one was born perfect when it comes to language. We say one thing when we mean entirely another. We mix up words, add endings, and pretend it’s all fine. Well, not quite.

However, sometimes the line between "wrong" and "neologism" can be blurry. Especially with things like slang. Like, a while back, people started using the word "sick" to describe something that's awesome. As in, "Sick tats, bro." Presumably the tattoos in question aren't ill; the word was adopted for its sound, and even us old folks could figure out what it meant.

But some things are wrong and will always be wrong, like using it's for its, or saying "literally" when all you want to do is add emphasis.

So this time, we’re gonna look at the most common mistakes we make when using these phrases, and hopefully, learn something that would have made our English teachers proud.

Snort. Some English teachers make these mistakes, too.

Anyway, there's 30 of them, and they're in short-attention-span meme format, so it wouldn't take long to go through them all. Which is why I'm not going to laboriously type any of them into here. That would literally be a waste of my time.

Instead, I'll let you go look at that if you like, but first, something I've been putting off because I was doing the MB contest and I didn't want to throw too much extra into blog entries.

One-Sentence Movie Review: Free Guy

Free Guy is a nonstop action comedy movie full of enough reference jokes to appeal to hardcore and casual gamers as well as other entertainment fans; the CGI is as lush and striking as you could possibly expect, and the writing and acting are right on target, and it even manages to dance around some interesting philosophical concepts -- it's no spoiler to reveal that this movie features a video game NPC gaining sentience and trying to save his world (it was in all the previews), but in the end, the most unrealistic bit in the movie is the romantic subplot.

Rating: 4/5

3 Like • Comment • View 5 comments

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