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 2 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 4 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 8, 2023 at 7:24am

#1042807

Greetings from Asbury Park, NJ

...or close enough. Can't resist the Springsteen reference.

I'm just here overnight, and then it's back to NYC for a couple of days before I head home.

I really like beach towns in the winter. Well, to clarify, I despise winter. Too cold. But yesterday wasn't that cold, so I actually spent a couple of minutes (shudder) outdoors. Not walking on the beach, though. I hate walking on the beach no matter the season. You know how everyone's dating profile says "loves long walks on the beach?" Not mine. Well, if I had one, it wouldn't contain that line. There's not much that annoys me more than sand in my shoes. Walking on a New Jersey beach barefoot isn't recommended, either. In the winter, it's too cold; in the summer, it's too hot; and in every season, it's too used-needly.

Still, beach-adjacent is pretty cool. Last night was just a day after a full moon, which means that to a casual observer, it might as well be full. Also being a full moon, it hovered above the Atlantic after rising, and honestly, if you've never seen the moon reflected on the ocean, you haven't lived. Often known as the Wolf Moon, it's not, as most sources assert, necessarily the full moon of January, but the first full moon after the solstice. Didn't look like a wolf, though. Just looked like a moon.

One thing I particularly enjoy about beach towns in the winter is that restaurants tend to be less busy—the ones that stay open, anyway. It's more relaxed, fewer tourists (I'm not a tourist; I'm a visitor), and even if the food isn't as fresh, at least it's prepared with more care. Sometimes, if you're really lucky and hit it at just the right time, you're the only one there.

The one we went to yesterday, though, was damn near packed. Disappointing. Food was still delicious; it's been a while since I've had linguini with clams, and what better place than the shore? Well, okay, there are probably better places to eat seafood than the Jersey Shore, such as "anywhere else." I've even had good sushi in Iowa, and that's almost as far from the ocean as it's possible to get in North America. Anyway, whatever; it was good and barely tasted like mercury at all.

4 Like • Comment

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