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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Write_Mikey_Write!

about 8 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 10 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.

January 28, 2024 at 9:27am

#1063091

Revisited: "Who"

Today is my regular trip to the past, and I landed by chance on an entry that's definitely worth another look. It's a good time for this to have come up in my random pickings: "Who"

It's from October of 2018, and it's about the show Doctor Who; a rare, for me, opinion on pop culture. I've learned not to give out too many of those, because I almost always get burned. Praise an actor? Turns out they're a pedo. Say something good about a show? It goes downhill. That sort of thing.

Anyway, let's see what I said then and how things are going now.

So... I've seen every episode of Doctor Who.

Still true.

Well, I haven't gotten around to watching the recreated 4th Doctor episode Shada yet, but as it never aired when it was made, it doesn't really count.

Bit over five years later and... nope, still haven't seen that.

There's been a lot of hype about the most recent incarnation, which premiered Sunday.

There is, of course, always hype. The difference then was that the actor was a chick, which angered the usual assholes, which pleased me.

The reason this older entry is appropriate now is that they just introduced a new Doctor again. Well, there were shenanigans when 13 regenerated into 14, who was actually 10 (David Tennant) for a couple of specials, but now they're on 15, who's a black dude, which angers the usual assholes, which pleases me.

Anyway.

New Doctor, new companions, new composer, new showrunner...

Yeah, now, the composer and showrunner have reverted to the folks behind the 2005 series revival, and this is a good thing.

Well, I'm here to tell you that the 13th Doctor *is* The Doctor. Thoroughly, completely, without a doubt. She nailed it. The other actors nailed it. The writers nailed it.

I stand by my opinion on Jodie Whittaker's first episode. The rest of her stint as the Doctor, though... well, it had its ups and downs, but I wasn't all that impressed by the writing or directing (though the acting continued to be solid, an actor can only do so much with a mediocre script). It wasn't bad; it just didn't really hook me.

Of course, now that I've posted this, the rest of the season might very well suck.

Many people seem to have only two opinions about anything: "That's awesome" or "That sucks." Long ago, Netflix had a star-rating system like we do here on WDC. I liked that, because you could express opinions in the middle. Have some nuance. Unfortunately, we now live in a world where many people seem to think that anything less than five stars means something sucks, and Netflix changed their rating to "awesome" or "sucks" (with the usual thumb icons).

There's nothing wrong with three stars. And that's what I'd give the 13th Doctor's run if I were asked (or, because it's my blog, I don't have to be asked). It didn't suck. It wasn't awesome. Those aren't the only choices.

I'll keep watching.

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