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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QPdoll

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I hope you're enjoying every minute in France! What an opportunity.

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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.

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WakeUpAndLive️~Happiness

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

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WakeUpAndLive️~Happiness

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

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Elisa: Middle Aged Stik

a day ago
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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

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WakeUpAndLive️~Happiness

a day 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/

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

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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

Sep 20, 2024 at 9:08am
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!))

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November 5, 2023 at 9:07am

#1058937

Revisited: "60 More Years!"

For anyone coming in new here, I like to highlight random past blog entries on Sundays. Why Sundays? Well, why not? I like to talk about how things, their context, my opinions, etc. have changed since I wrote the original entries.

Today's comes from a very long time ago indeed: June 3, 2008. "60 More Years!"

For context, as the entry notes, we here in the US were in the middle of the chaos of an election year.

I don't talk about politics much in here. I used to mention it more, in that time period, but at least I wasn't overtly taking sides in that entry.

Me: In other words, five more months of whose hair is better-groomed and which candidate's grandmother or great-grandmother was a flapper during the Roaring Twenties, because, of course, that makes a huge difference in who should be president.

Turns out that my grandmother, who was around 30 years old at the time, was a flapper during the Roaring Twenties. I don't remember if I discovered this fun fact before or after I wrote that blog entry.

But enough about politics. Let's take a closer look at one of those flyover states: South Dakota, land of... land of... um. What the hell is in South Dakota?

At the time, I'd never set foot in South Dakota. Between then and now, I've visited maybe three times? I don't mean "drove through," though I did, but I also sightsaw. Last time, I was stranded there for three days, but I covered that fun incident when it happened in 2021. However, during none of my trips have I visited the main subject of that 2008 entry. Not yet.

Ah, yes. The Crazy Horse Memorial which, as it happens, was begun sixty years ago today

I question my grammatical choices at the time, but whatever. From math, I deduce that the onset of construction of the memorial was over 75 years ago now.

There follows a raw link which, not surprisingly for a 15-year-old link on the internet, is well and thoroughly broken. Apparently, it was a retrospective on the 60th anniversary of the monument's official beginning. If you're not familiar with this enormous project, here's the Wikipedia link.

There's not much else to the blog entry, but I will say this: upon re-reading this today, it was too easy to interpret the last lines as a tribute to General Custer. While it's difficult to remember much about something I wrote a decade and a half ago, I'm certain that wasn't my intention. I should have phrased that better.

I'm tentatively planning another one of my cross-country road trips for the end of the month and on into December. Maybe, if the weather works in my favor, I'll pay a visit to the Crazy Horse Memorial.

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