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:

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.

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').

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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

February 7, 2019 at 1:14am

#951375

Mindless

Gotta take a break from the blog challenge. It's a great activity, but I have a backlog of blog fodder to share.

For instance:

https://www.marketwatch.com/story/avoid-these-3-traps-when-talking-to-someone-wi...

Avoid these 3 traps when talking to someone with dementia

I've noted this before, but for any newcomers, I lost both of my parents to long bouts of dementia. All told, I spent 20 years of my life dealing with one or the other. There are few things that frighten me more than the prospect of losing my mind (though I'm sure some would say that's already happened). Compared to that, death seems easy.

Everyone dies. What's hard is that some people die while their bodies live on.

Before you ask, no, I'm not all that concerned about genetic predisposition. I have no idea what my genetics are, and I prefer to keep it that way.

Anyway, I wish I'd seen something like this article before my parents started slipping away.

You’ve got great social skills. You speak clearly and listen well. Everyone loves your engaging personality.

Obviously, it wasn't aimed at me, anyway.

Prepare to encounter speakers who repeat themselves (asking the same question every few minutes) and make illogical statements or faulty observations. Their emotions can swing wildly from moment to moment, leaving you wondering what could’ve triggered an angry outburst or crying spell.

This is true.

Say the individual ponders the whereabouts of their spouse. If you point out that their spouse has died, that may be true but unhelpful.

That seems obvious, but I can be oblivious. Now, I may have spent my life in the Regretium mines of Regretistan, but the one regret that stands out to me above all others is the time when my father did exactly that. And I answered without thinking. Or feeling.

My parents had been together for nearly 60 years when my mom died. They weren't in what I'd now call a functional relationship, and yeah, I'm dealing with the psychological repercussions of that (just like everyone else is), but they stuck together anyway. When my dad had no choice but to seek a suitable care facility for her, he went to visit her every goddamn day.

I can only hope that he quickly forgot the incident, along with my name (which is something that he was always kind of fuzzy on anyway) and, later, everything else. But I never did.

Yeah, I'm putting this out here in hopes that I can move on. Still, I could have been better. It wasn't out of anger or frustration, or anything like that - at least I don't think it was - but rather just thoughtlessness on my part. I wrote here some time ago that I feel I should work on being more compassionate; this is why.

I'll say this, though. Some people think that Alzheimer's and similar conditions strips a person to their bare essence. I've seen a lot of people with dementia getting angry, lashing out, becoming violent and hateful, like their public face is but a thin veneer hiding some horrid monster. Honestly, I don't know - I think we're all part caring and good, and part spiteful and angry, all at the same time. We are large; we contain multitudes. But in all the times I visited my father in his final years - which, admittedly, weren't as many as I should have - I never saw his dark side (and when he was in his prime, he definitely had a dark side). I'd sit down while they were eating, and he'd offer me some of his meager food. One time he saw I wasn't wearing a coat and insisted I take his. This was true even when he didn't know who I was.

Why am I terrified of dementia? Well, partly because when I'm weighed in the same balance, I'll be found sorely wanting.

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