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 12 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 14 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.

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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').

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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.

May 20, 2020 at 12:15am

#983963

Mind Games

If I thought I was going to live to 90, I might do some things differently.

PROMPT May 20th

If you were able to live to the age of 90 and retain either the mind or body of a 30-year-old for the last 60 years of your life, which would you choose?

I mean, if you've been following along, my answer should be really obvious.

Still, I have to say it depends. Do I get to pick the 30-year-old? Can she be hot?

Seriously, though, it depends on what's actually meant by "the mind of a 30-year-old." If I were writing a monkey's paw story where someone wishes to retain the mind of a 30-year-old for 60 years, I'd probably get them stuck at age 30 in terms of not being able to learn anything new. With age comes experience as well as some loss of mental flexibility, and it would really suck to keep the flexibility but be unable to use it.

I'm not sure if I'm explaining this right. I spent five hours on the phone today, mostly on hold, trying to get an account sorted out at the bank. That hold music is now etched into my synapses until the end of time. When I finally got it sorted, I drank to try to get the muzak out of my brain. In that, I was only partially successful, and now between the earworm and the lingering aftereffects of an entire bottle of really good red zinfandel, I'm not sure I'm thinking straight.

Anyway, let's not do the monkey's paw thing and assume that by "the mind of a 30 year old" it's meant to be mental flexibility, learning ability, neuronal plasticity, all that. Well, then, definitely that. I'm way more focused on mental pursuits than physical, anyway, and after seeing both of my parents gradually deteriorate from dementia before age 90, I know for certain that I don't want to go there myself. I'd rather be physically feeble and mentally alert than mentally feeble and physically hale.

While sex would be better with the latter, that's not going to happen with me anyway, so why bother?

All of this, of course, assumes that it's truly a binary choice, like the one a while back that asked if you had to lose either hearing or sight, which would you choose. If a genie popped out of one of my beer bottles and told me those were my only choices, I'd ask for another beer instead. I mean, life is life, right? Cheating isn't any fun.

5 Like • Comment • View 8 comments

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