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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Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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.

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Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

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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.

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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.

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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.

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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.

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February 28, 2019 at 12:43am

#953345

Journeys

Finally, the last day of the hated month of February.

Unfortunately, the weather report here indicates more cold days ahead, and possibly s**w. But at least the end is in sight: three weeks to the equinox.

If I can make it that far without straying too far from my healthy-eating-and-exercise plan, begun on the solstice, I'll consider it a win. Then it won't feel so bad when I inevitably fail.

I've been waffling about whether I want to reprise the "30-Day Blogging Challenge ON HIATUS"

[13+] in March - though I'm leaning toward not doing it this time. That merit badge up there

is from winning it in January; while I'm not focused on winning, I originally started doing it as motivation to blog every day, and I think I can do that anyway, writing about the subjects that interest me and not necessarily following a prompt. Still, it can be a great activity, and I highly recommend it for anyone who wants that extra motivation.

Besides, I might need to give myself permission to skip a day or three in March. Perhaps I'll re-evaluate for the next round, presumably in April - though I might have to go to NYC for a few days then.

In other "win" news, back in December, I signed up to do "I Write in 2019"

[E] - one contest entry and one review per week. I've actually been successful at that as well - at completing the tasks, anyway. We'll see if that holds up. It's going to be especially tricky in October and November, what with NaNo and Prep, but I'll burn those bridges when I get to them. Again, I expect to fail eventually - so I can't be too disappointed when it happens.

I'm starting to get antsy for travel again, too. Part of that, though, is the crappy weather we've been having (normal for February in Virginia, but still crappy), so we'll see if I still have the urge in, say, April. I'll be unsatisfied if I don't go somewhere this year; I just don't have any firm plans yet. Maybe in conjunction with my possible NYC trip. Probably another beer tour; if so, that will automatically fail my health efforts - at least while I'm traveling.

I mean, losing weight is great and all, but beer is more important.

6 Like • Comment • View 4 comments

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