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!

a day 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

a day 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.

July 29, 2019 at 12:04am

#963344

July? No, I Mostly Tell the Truth

Reflect on the month as a whole. Any highlights from your personal life? Challenges? What were your favorite prompts from the 30DBC? Did you learn anything from or about your fellow competitors?

Highlights from my personal life: Against all odds and expectations (specifically, mine), I stuck to my eating plan and went to the gym every damn day, even though I seem to be developing a massive pain in my left foot. That is bullshit; after losing more than 60 pounds in seven months, I expected my feet to hurt less. Come on! Okay, I may have cheated on the eating thing once, because a friend was in town and I can't say "no" to a pastrami sandwich for very long (and there was beer), but you know, I lost weight anyway. So there.

Challenges: Look, I'll be honest here; I build my life around avoiding serious challenges. About the worst thing that happened to me was the power went out one night. I have a backup generator that kicks in after less than 30 seconds, but I can't seem to be arsed to put my router on an uninterruptible power supply, so the internet was out for a few minutes, while I was trying to do something here. Seriously, that was my biggest challenge so far in July, apart from the Great Pastrami Sandwich Temptation, which I failed at miserably and deliciously. (As a pessimist, I have to note that there are still three days left in the month, plenty of time for the stock market to crash or my house to burn down.) The weight loss thing has turned into a habit, not a challenge; and I don't count writing challenges like this blogging thing or weekly writing activities, because I chose those for myself.

Favorite prompts from the 30 Day Blogging Challenge: Gotta admit, I had a lot of fun with several of the prompts. The one I'm most proud of is throwing together an abecedarian poem, complete with rhyming couplets, in less than two hours, back a few entries ago. Besides, I got to think about, if not drink, beer for that one. The news story one was fun too, because that's more in line with what I do here when there's not a challenge running.

My fellow competitors: I enjoyed reading others' blogs this month, even if I didn't get to all of them because of timing. I should note that I'm not a "competition" person; I consider this a shared journey. But I feel like I got some insight and understanding into others' perspectives. Thanks for the trip, everyone!

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