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 9, 2021 at 12:02am

#1022986

In Spite Of

Few things in life feel better than nuclear revenge. So today's link is about the lengths (or heights) some people will go to for it.

38 Things Done Out of Spite

I mean, sure, it's nice to be able to forgive sometimes, too. But other times, you need to drive the point home that you're not a pushover.

Most of these are spite houses / fences, but there are a few other cases of extreme -- and mostly legal and nondestructive -- payback as well. I won't go through all of them; you'll have to check out the link.

4. Stuart Semple's Black 3.0

This one's one of my favorites, mostly because I find feuds in the art world extremely amusing, and also because I want an outfit, preferably including a trenchcoat, made of the blackest black that ever blacked.

The color war began when artist Sir Anish Kapoor acquired the exclusive rights to the world’s blackest substance at the time, Vantablack—and refused to share it with the artistic community.

By all accounts, Kapoor acts like a massive douche. He's the artist (and I'm not denying he's a talented artist) responsible for The Bean

in Chicago. Since he's apparently gotten used to people calling it The Bean (or maybe he just backed off on public hatred of the name so people would leave him alone), we'll have to come up with another annoying nickname for it.

Enter British artist Stuart Semple, who, angered at Kapoor’s selfishness, created the “pinkest pink” and made it available for anyone to use … except Kapoor. Purchasers were obliged to agree to a statement that read: “By adding this product to your cart you confirm that you are not Anish Kapoor, you are in no way affiliated to Anish Kapoor, you are not purchasing this item on behalf of Anish Kapoor or an associate of Anish Kapoor. To the best of your knowledge, information and belief this paint will not make its way into the hands of Anish Kapoor.”

Like I said. Art feuds.

18. A Spiteful Christmas Display

When you're on the front lines in the War on Christmas...

19. The Hollensbury Spite House

Constructed in 1830, what’s now known as the Hollensbury Spite House is just 7 feet wide and contains 350 square feet in its two stories, or “about as much space as a large outdoor billboard,” according to the Washington Post.

I haven't seen this particular building, but 350 square feet in Alexandria? It's probably worth about 3 million dollars.

22. Castle of Spite

For when you're extremely wealthy AND hostile.

Anyway, most of these are interesting for one reason or another -- family drama, libertarians vs. City Hall, thwarted romance... all the stuff worthy of stories.

I guess that to err is human, to forgive is divine, and to create something out of spite is deeply satisfying.

4 Like • Comment • View 5 comments

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