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 8 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 10 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').

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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.

January 7, 2024 at 7:27am

#1062008

Revisited: "Procrastination"

Today's spin of the roulette wheel (which is actually redundant, as roulette is probably translated as little wheel, so that would make it a little wheel wheel) brought me all the way back to January of 2007, not long after I started this blog. And it demonstrates why I've never really gotten anywhere with my writing: "Procrastination"

I've been kicking myself for procrastination for far longer than that, though, but have never managed to stop actually procrastinating. As I've finally recognized it as a core feature of my personality, I've now given up trying to change.

Or, I don't know. I keep meaning to. Maybe next week.

As for the entry itself, it begins with what's now an Invalid Item link. What used to be there was a Daily Writing Challenge, which was an activity I found useful in prodding me to complete daily writing exercises. As I recall, it started out with just a few words, and gradually worked up to 2000. Kind of like that guy who lifted a calf every day. The calf kept growing, but he didn't notice because he got stronger. Until, one day, he's walking around with a full-grown ox on his shoulders.

Left out of that story was how the ox might have felt about being used that way, but I imagine it's better than being yoked to a plow.

Oh, yeah, Milo of Croton

was the dude's name. I think he was a real person, but the ox thing was almost certainly mythological.

From the entry:

I'm sitting here procrastinating. I know once I get into the writing, it'll go fairly smoothly. Still, I'm putting it off like I always do with stuff. I had hoped I would learn better by now.

Nope, Younger Me: you never do learn better. You just learn to live with it.

Oh, and then there's the Fiction Writing class I signed up for. It begins Monday, and runs for like 9 weeks, once a week.

I vaguely remember that class. It was a continuing education thing at the university. I remember they sneered at me for writing science fiction. Snooty lit-snob poseurs.

Okay. Enough with the procrastination. Time to write.

Well, maybe some dinner first...

Anyone else writes that, I assume they're joking. I was not. That is truly how my mind works. Or, well... doesn't.

4 Like • Comment • View 3 comments

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