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!

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').

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.

November 7, 2019 at 12:15am

#969163

None More Black

PROMPT November 7th

What is your favorite color? Do you have a favorite color pairing? What’s something in your life that you picture when you think of your favorite color? Do you choose to wear clothing that is your favorite color? Has your favorite color changed over your life?

Use these questions to explore how your favorite color has influenced you.

What is your favorite color?
Black.

Do you have a favorite color pairing?
Black with More Black

What’s something in your life that you picture when you think of your favorite color?
The Void.

Do you choose to wear clothing that is your favorite color?
Almost all the time.

Has your favorite color changed over your life?
For a while in high school, I thought my favorite color was blue, but no, it was still black.

"But Waltz, black isn't a color! It's the absence of color!"

Black is a color. It's technically an achromatic color, a color without hue. An object that is black doesn't radiate much in the visual spectrum (in the case of black holes, not at all), and it absorbs all visible light that impacts it. It probably generates or reflects other frequencies on the EM spectrum, though; we just can't see those.

Some scientists a while back came up with a material that's nearly 100% black; it's so black it's hard to look at. Sadly, they didn't make me a t-shirt out of this material, but licensed it to some idiot artist.

I'm a lot of fun at weddings, let me tell you.

My affinity for black has little to do with its cultural associations, though. Mostly, I just think it looks good. Partly, it has to do with science, in some sort of metaphorical sense - as a black object absorbs light, so I absorb knowledge, however imperfectly.

It's not the only color I wear, but its primary sartorial advantage is that it pairs with almost anything, which is useful when you don't want to ever think the sentence: "What color shirt will work with these pants?" So my traveling outfit consists of black shoes, black jeans, a black t-shirt, and the loudest Hawaiian shirt I can find.

People should sigh in relief that at least I don't pair the Hawaiian shirt with striped pants.

6 Like • Comment • View 10 comments

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