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:

Writer_Mike

about 9 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

a day 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.

2 Like

Annette in France

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

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day 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

a day 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

a day 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

Sep 21, 2024 at 6:46am
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

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

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

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
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.

March 12, 2023 at 12:39pm

#1046275

Revisited: "WTC"

So Daylight Slaving Time has started now. Here, anyway. Not everywhere, thus leading to mass unnecessary confusion.

Speaking of time and confusion, my random generator gave me yet another entry from 2009, part of a series of blog entries expanding upon a list of things to know about Me.

Clear? Good. The entry is "WTC"

.

The bit of Me-trivia at the beginning:

14. I stood atop the World Trade Center when there was a World Trade Center. I don't remember if it had a 13th floor.

Which really doesn't make complete sense unless you know that the previous entry started out with "13. I chuckle whenever I see a building that doesn't have a 13th floor."

I've rambled about 13 fairly recently; no need to bring any of that up again. Back to today's highlighted entry:

Actually, I was there two or maybe three times. Fantastic view when the weather was clear.

At least once as a tourist, and once on business. The tourist thing took me to the observation deck, which was cool. The business thing (I was running errands for my aunt) was actually kind of more interesting, because I got to see parts tourists usually didn't.

Now... there's a link at that site. It's dead. (Actually, both links are dead.) The purpose of the link was to show that I'd discovered that the WTC towers did, indeed, have 13th floors. Before you go saying "See? Obviously it was unlucky," consider this sole surviving quote from the now-dead link:

Both towers of the World Trade Center had occupied 13th floors and, ironically, after hijacked planes slammed into the twin towers on that fateful day, media accounts of harrowing escapes told of many rescues from the 13th floor of both the North (1 World Trade Center) and South (2 World Trade Center) towers.

For those survivors, luck began on the 13th floor.

Well, first of all, actual luck would have involved not having the towers collapse. Second of all, that's flagrant misuse of "ironically." But still, an interesting take on things.

In reality, the number 13 had fuck-all to do with the events. The important thing is that I Was There. Just not on that day. Lucky me.

6 Like • Comment • View 3 comments

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