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 6 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 8 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.

July 8, 2021 at 12:02am

#1013272

Fortunately

Well, I made it home. In an amazing stroke of (further) luck, every flight -- there were three of them -- was on time or ahead of schedule. I seriously need sleep, but I figured at least I could stay up long enough to get today's blog entry in.

And what better way to commemorate a trip cut short by the slings and arrows of outrageous fortune than to do some entries for "JAFBG"

[XGC]?

I don't know if I'll do every prompt; there are 20 of them in the current batch. But, true to my usual methods, I selected one at random for today. Here it is:

What's stopping you from helping those less fortunate than yourself?

Almost everyone is less fortunate than myself, so I guess... the sheer magnitude of the contemplation thereof?

"But Waltz, your car just got ungulated into oblivion; how can you say you're fortunate?"

Glad you asked. As I noted a couple of entries ago, shit happens. Life, I think, isn't about the shit that happens to you, but about what you do in response. Into each life, some shit must fall -- to misquote the old song -- and it helps to be prepared and keep your head about you when it does. And I was prepared, and lucky -- another word for "fortunate."

To get back to the prompt, though (I mostly did that aside so I could show off my new verb), I know I've talked about this sort of thing before; that is, the concept of charity, or alms, or aid to the needy (however "need" may be defined). And I've said I don't like to talk about it, because I always feel like I'm boasting or virtue-signaling or putting some sort of good-deeds trophy on metaphorical display.

Not that I haven't talked about it, which is how I know I don't like talking about it (unlike talking about my occasional linguistic brilliance). So for the purposes of this entry, let's just assume I'm a self-centered prick who doesn't give a fuck.

I've also noted before -- probably in the same entry -- that there are causes I won't donate to, such as anything with the word "Family" in the name, or any group that tries to guilt me into giving at a checkout counter. Even assuming that some of those groups do some actual good in the world, which they might, what's stopping me is their tactics -- hiding behind the supposed welfare of children, or attempting to shame me if I don't say "yes" when some checkout person asks if I want to donate a dollar to the Give Some Kid A Hot Lunch fund or whatever.

Incidentally, I know it's probably just as uncomfortable for the cashier to keep asking that. Probably even more so. It's not their fault; they have to ask or risk losing their job. I'm sure some of them wish someone would start a fund to help them out.

And don't get me started on Girl Scout cookies. Actually, no, this is a JAFBG entry so go ahead, get me started on them. I have no issue with the Girl Scouts in general. But one day, walking on Fifth Avenue in Manhattan, I came upon their headquarters. Like I said, it's on freaking Fifth Avenue, in midtown, not too awfully far from the Empire State Building. Not exactly cheap real estate. No, it's the polar opposite of cheap real estate. I'm pretty sure they could build an underwater habitat dome for their headquarters, and it would cost less than a skyscraper in goddamn midtown Manhattan.

The point being that they already have money, and pressuring family, friends, and people trying to get groceries to cough up five bucks a pop (or whatever the street value of those drugs are these days) is like making the US military hold a bake sale to finance their next battleship.

Which actually sounds like a good idea.

Anyway.

Yeah, I know I'm talking specifically about monetary donations, but the same sort of thing applies to donations of time/labor. For instance, I'd hate to volunteer for something only to find out that the board of the foundation, or whatever, is getting paid six figures or more for their "efforts."

So I guess the real response here, for me, is that I have to be sure it's something I'd consider a worthy cause. Not just the cause, though, but their structure and methods. If I feel like it's a scam, by my own reckoning, then that will keep me from helping them. No, I'd rather help the needy directly -- assuming that I, the self-centered prick as described above, would even want to -- than funnel it through a group that skims half the donations off the top.

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