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 13 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 15 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.

May 6, 2020 at 5:51am

#982882

Memories

I may have overdone the cultural appropriation of Cinco de Mayo yesterday. My stash of tequila is almost gone. This would be a crisis if I didn't have plenty of other beverages; I'm about done with tequila for at least a few days.

PROMPT May 6th

Write about an object you own that has negligible monetary value, but is priceless to you.

I'm usually wary of revealing stuff that people could use against me if I inadvertently piss them off, so the temptation is there to make up something about a RealDoll. Those things are expensive, or so I've heard, but the used RealDoll market is, understandably, nonexistent. So it would fit the bill quite nicely.

If you've never heard of a RealDoll, congratulations. I strongly suggest you don't Google it.

On a philosophical note, if something has negligible monetary value, can one truly say that one "owns" it? Can a person truly own anything, for that matter? And what is the sound of one hand clapping?

While we're at it, how are "worthless" and "priceless" antonyms?

I have a lousy memory, and I rely on objects to remind me of the past. There's a lot of past, so there's a lot of objects. Most of them are objectively worthless, but, at the same time, I probably wouldn't be overly emotional if they vanished.

For a while, I had a cat named Ghost. I met him as a kitten; he wasn't even a week old, and no one knew where his mother was. His eyes were closed, and he was utterly helpless, a little gray blob. At that age, without maternal care, kittens have a tendency to fail to survive. When he did survive, against the odds, that's when I named him. He grew into a tiger-striped gray tabby with a little white spot on the very tip of his tail.

He was my cat before I got married, and he was still with me after my wife dumped me, more constant than any human. He'd follow me on my walking adventures, taillight held high, and at night he'd stand sentinel at the foot of the bed.

A couple of months after I had a heart attack, Ghost also had a heart attack, at the ripe old age of 16. He was still alive when I rushed him to the vet; afterward, he wasn't.

His ashes, worthless and priceless, stand on a shelf, accompanied by those of my other good kitties, their memory guarded by a statue of Bastet.

I lack the genes that prompt some people to need to have someone to take care of, or to need to have someone to take care of them. But for a while there, Ghost and I took care of each other, and it's nice to have a memory of that.

5 Like • Comment • View 5 comments

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