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 13 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 14 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.

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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.

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.

May 23, 2020 at 2:20am

#984143

Weird

It occurred to me recently that if you take anyone who is doing anything and imagine them doing it in the dayroom of an inpatient mental hospital, they'll fit right in.

PROMPT May 23rd

What is something you like to do that other people might think is “weird?”

The above thought came to me just yesterday, in fact, as I was taking my (almost) daily walk around the neighborhood. See, the gym is closed for obvious reasons, but I didn't want to quit exercising entirely (as tempting as it was to consider it), so I have a 30-minute loop I always go on. Except when it's raining hard. I'm not a masochist.

I offset any health benefit from this by smoking a cigar on the way. The primary reason I do this is that it tends to keep people out of my face. This is of great use to me now because it's an automatic social-distancing enforcement measure. I didn't much like interacting with random strangers beyond a "Hi, how's it going, great, have a good one!" anyway, so the pandemic has been a real boon to me. Yesterday was the first Really Nice Afternoon we've had in a long time, and the first time that strange glowing orb appeared in the sky in about a week, so a lot of people were out. It was actually quite heartwarming to see a woman, mother-sense tingling, snatch her kid off the sidewalk in front of me while glaring at me for a reason other than merely "warning pervert approaching danger danger."

But really, lady, I'd have gone around.

So that's one thing for the prompt. Cigars during exercise. I mean, it's not like I inhale.

Pretty much every second house in the neighborhood had someone outside it, though. It was a Friday afternoon, so it probably will be even more active today. The rain had just quit so no one was mowing, but other yard work was getting done, balls bouncing against garage doors, wrenches turning under cars, folks sitting in beach chairs. You know -- perfectly normal, suburban single-family-detached-home-neighborhood activities (though technically I live in a city, not a suburb), each and every one of which, if taken out of context and placed into a mental institution, would confirm to an observer that the individual is exactly where they need to be.

So do that mental exercise next time you're out doing people-watching for "research" for you next "book." Imagine each individual in the dayroom doing the same activities. I should emphasize here that I'm not shaming mental illness or making light of it; quite the opposite, in fact. Apart from violent patients, I'm pointing out that the line between "normal" and "weird" behavior is often blurry, and a matter of context and setting. Also, I feel the need to note that I haven't actually been in a mental hospital so I'm only going by 50 years of movies and TV shows. I always wondered about the extras they always get for those dayroom scenes. Having dabbled in acting myself, I think the background actors probably consider it the most fun they can have at work, with or without their clothes on.

As a final note, the word "weird" is weird. Not only is it one of the many exceptions to the well-known "I before E except after C" rule, but it's one of those words, like "nice," that have changed meaning over time. It used to denote a person's fate or destiny; the Fates were called "the weird sisters" not because they were strange, but because they were considered to rule destiny. Merriam-Webster

has this to say about it:

You may know today's word as a generalized term describing something unusual, but weird also has older meanings that are more specific. Weird derives from the Old English noun wyrd, essentially meaning "fate." By the 8th century, the plural wyrde had begun to appear in texts as a gloss for Parcae, the Latin name for the Fates—three goddesses who spun, measured, and cut the thread of life. In the 15th and 16th centuries, Scots authors employed werd or weird in the phrase "weird sisters" to refer to the Fates. William Shakespeare adopted this usage in Macbeth, in which the "weird sisters" are depicted as three witches. Subsequent adjectival use of weird grew out of a reinterpretation of the weird used by Shakespeare.

Pretty weird, yes?

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