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 5 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 7 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.

April 9, 2024 at 6:24pm

#1068297

Dark Side of the Moon

Made it back home. Amusingly, the weather did clouds and rain the entire 8-hour drive back—which, fortunately, didn't happen yesterday.

If you're hoping for a description of the eclipse, look elsewhere; it's been covered by better writers, and better photographers, than me, so I won't even bother. Just know that, whatever you've read, it's insufficient to describe the experience; and whatever pictures you've seen cannot do it justice.

I've seen some scoffs on the internet to the effect of "why bother with the hassle of traveling when you can watch it on video online?"

Leaving aside how sad their lives must be, or how it might feel to have one's sense of wonder surgically excised, I have to wonder if they ask that about everyone's experiences:

"Why go see a band in concert when you already have all their albums and can listen to them anytime?"

"Why bother going to a football game when you can watch it on TV?"

"What are you doing going to Disney World when you can watch internet videos of the lines and rides?"

"Why go camping when you can just look at pictures of trees and rocks?"

Now, granted, you won't catch me doing the last three, and my days of doing the first one are probably behind me, but I try not to yuck other peoples' yum.

Maybe some of them are just trolling. Maybe some honestly don't see the point in viewing celestial phenomena, and would rather go to concerts, sports games, amusement parks, or the (shudder) outdoors. Maybe an eclipse is "nerd stuff," but the fact is, everyone's a nerd about something. If it's not astronomy, maybe it's music, sports, theme parks, or hiking. Or beer or wine. If you really like something and seek its experiences and knowledge, you're a nerd about it.

As for me, I ended up seeing it from the grounds of a winery in Indiana, which may sound odd, but I'd been to that particular one before, and I knew they had good product. My friend and I got lucky that, when we got there, they still had viewing spots available, and we even got bling bags out of the deal. And they played Pink Floyd as the eclipse progressed, so everything came up Waltz. No, I didn't have detailed plans beforehand; I didn't see the point when, had it been cloudy, all that planning would have been mostly wasted.

Sick of hearing about the eclipse? Don't worry; that was very likely my last one, so no more from me on the subject... probably. Tomorrow, back to my regularly (and randomly) scheduled nerdery.

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