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 an hour 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 3 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 7, 2023 at 9:42am

#1049327

Revisited: "No Fault of Mine"

As it is Sunday, I'm once again delving into the past to see if anything's changed and, if so, how.

Another relatively recent one popped up (though I'm still limiting my retrospectives to exclude the past year), this one from my trip to SoCal early in 2022, when I visited NaNoNette

and her family: "No Fault of Mine"

It's a short entry and, since it's not very old, I only have a bit to expand upon.

We took a drive around a place that's known for its landslides, marveling at all the doomed houses all built to appreciate a view of the ocean. I'm thinking a lot of them will get a much closer view of the ocean at some point. Oh, and did I mention there's also a fault line involved? Fun!

I'm thinking this may have come across as joy in the misfortune of others. That wasn't my intention. While I'm not above a bit of schadenfreude from time to time, I normally reserve it for people I think deserve it for some reason. Just living in a place that you know is subject to seismic events doesn't qualify; there is no place that's not subject to the looming threat of disaster. If not earthquakes, then wildfires, tornadoes, fire tornadoes, sinkholes, meteor strikes, enemy missiles, avalanches, hails of gunfire (mostly limited to war zones and the US), floods, droughts (sometimes both at the same time), and that perennial favorite of the Atlantic coast, hurricanes.

And lots of people don't have the luxury of being able to move, even if there is a safer spot to move to.

My point is, life is uncertain and I can't fault (pun intended) someone for trading a nice view and generally wonderful weather for the possibility of sliding into the Pacific at some point.

In that entry, I spoke of my plans to visit Catalina, a lovely island off the coast near L.A. I did, indeed, manage to get there, and wrote a bit about it in the following entry.

Lastly, the link to the Wiki page for Santa Catalina Island is badly formatted; I have no idea if it broke in the past year or if I just didn't bother to double-check it because I was in a hurry. It's easy enough to get there with a couple of extra steps after clicking on the link, but here's an xlink anyway.

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