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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Wordsmitty ✍️

about 2 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

1 Like

Annette in France

about 13 hours ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

about 16 hours ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

about 17 hours ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

about 22 hours ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

about 22 hours ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

about 23 hours ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

a day ago
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

Cubboo!

a day ago
In response to "Get Baked"

Yes! I discovered this a few years back (slitting the potato about 1/4 - 1/2" lengthwise, then one or two slits across the longer slit.) It came out wonderful! It seems like this was called an English jacket potato, or something like that.

2 Like

April 14, 2024 at 7:19am

#1068727

Revisited: "Getting the Lead Out"

Today's historical excavation takes us back to 2019, at a time when I was apparently participating in the 30-Day Blogging Challenge... though I neglected to note that in the entry: "Getting the Lead Out"

For context, my current >4 year daily blogging streak wouldn't start for about another month, and, obviously, this was in the Before Time.

The prompt I was writing to started with "What characteristics do you admire in a leader?" and continued to build on that. I'm not sure I really addressed all the nuances of the prompt, but I'm okay with that, especially now that it's >4 years later.

I am a Bad Example. I even printed up "business" cards with my name followed by "Bad Example."

My friend's ex-wife never liked me. She called me his "bad influence." I should have run with that, instead.

But I'm not always. Case in point: it might have been the month after this entry appeared, maybe not, but let me set the scene: California, the home of two of my friends, married to each other, and their kids. Breakfast time. Someone made pancakes. I poured a small amount of syrup onto said pancakes.

The mom, talking to the youngest kid, maybe 12 or so: "See how he doesn't drown the pancakes in syrup?"

The dad, to me: "Bet that's the first time you've been held up as an example of self-restraint."

Everyone involved, especially me, had a good laugh at that one.

Basically, I don't want to be a leader. I don't like it. The benefits don't outweigh the constrictions, for me. I admire those people who can do it...

I worded this poorly, I think. There are lots of people who are "leaders" that don't deserve, or get, my admiration, or even respect. Evangelical TV preachers, for example. Most politicians, from any political party. Certain billionaires. Thing is, those types get all the press. I'd be hard-pressed to cite an example of a leader I actually admire, at least in terms of naming someone well-known. Being well-known probably works against you, there; not one of us is without our follies and drawbacks, and being in the public eye tends to put a magnifying glass on them.

What I should have said was probably that I have some respect for those who can balance things well enough to be both a good leader and, mostly, still be what I'd consider a good person.

But there's one thing I hate more than being a leader, and that's being a follower.

Still true.

Fortunately, life isn't binary, and I choose Option C: going my own way. It's enough to be responsible for my own situation, and I'm not always so good at even that.

Not everyone has that option, I know.

Another thing I'm terrible at is motivating people. I like it when people motivate themselves. Any attempts I make in that direction always seem hollow to me. But I think good leaders find ways to motivate their team, though how they do it might as well be sorcery for all I understand it.

A few weeks after this entry, I did one on Emotional Intelligence, or EQ. I only remember this because I was skimming nearby entries while trying to remember the context of this one. I probably could have related the two concepts at that time, but I didn't. In summary, I question the whole concept of EQ because it seems self-referential: they define EQ as the quality needed to achieve success (based on a narrow definition of success), and to achieve that kind of success, you need a higher EQ.

My point being that I imagine it takes those same qualities to be an effective leader.

Anyway, yeah, this is kind of rambling, but the bottom line is: don't look to me to set examples, unless you enjoy drinking at bars.

Again, this was the Before Time, so the difference now is I'd end that sentence with "home."

1 Like • Comment

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