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 8 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 30, 2023 at 7:10am

#1047161

Can't Get There from Here

I've always had a desire to go places I'm not allowed. What's through that door? How's the view from that tower? Wouldn't it be cool to climb the cables of a suspension bridge? That sort of thing.

17 Forbidden Places You Can't Visit

I've never done it, though. I tend to follow rules.

Well, not never. I've never been caught, though.

Still, most of the things on this list don't trigger my wannago.

1. Ilha da Queimada Grande

Ilha da Queimada Grande, or “Snake Island,” is an island off the coast of Brazil that’s home to a rare and incredibly deadly species of snake called the golden lancehead... The snakes are so dangerous that the Brazilian government has forbidden people from visiting the area.

Right now, most of you are going NOPE NOPE NOPE NOPE. Personally, I think this would be cool (except for the venom part). I once visited a snake island near Antigua, and while the serpents there weren't venomous, a lot of people cowered in the boat. Me, I went actively looking for reptiles.

3. Ise Grand Shrine

The first iteration of this Shinto shrine in Japan was constructed around 2000 years ago, and since the late 7th century, it’s been torn down and rebuilt every two decades... While tourists can view it from the outside, the inside of the shrine is only accessible to the highest priestesses or priests.

This sort of thing is not uncommon in religion. Respecting it is one reason I tend to follow the "do not enter" rules. Still, I'd love to see it.

4. The Svalbard Global Seed Vault

No desire to go there. Not because it wouldn't be interesting, but because it's in fucking Svalbard.

5. The Vatican's Secret Archives

Established in 1612, the Vatican Apostolic Archive (formerly the Vatican’s Secret Archives) contains the personal documents of all the popes.

Fiction makes this place out to be a collection of everything the CC doesn't want the rest of us to know (which, in a way, it is), but the reality is probably far less interesting. Also, I'd wager few, if any, of the documents would be in the only language I can read fluently.

7. Uluru (Formerly Ayers Rock)

Following petitions from the Anangu people, the board of the Uluru-Kata Tjuta National Park finally announced plans in 2017 to ban hikers from the site for good.

Oh, good. Now do Bear Lodge (aka Devil's Tower).

10. Montserrat’s Designated Exclusion Zone

When the Soufrière Hills volcano awoke from dormancy in 1995, the nearby town of Plymouth was evacuated and eventually abandoned altogether as eruptions continued. Ash consumed the town, turning it in a modern-day Pompeii. While the volcano is not as destructive as it was a few decades ago, there’s a chance it could erupt again, which means more than half the island is still a designated exclusion zone.

I... well, I might have gone a foot or two (or maybe more) into the exclusion zone, just so I could say I did.

It remains the only active volcano I've watched (the ones in Hawai'i were inactive when I visited), so that's something, anyway.

12. Area 51

There are lots of places I won't go out of respect for the people involved. Then there's this place, which I won't go to out of respect for not wanting to get shot.

17. The Ethiopian Church That Claims to Hold the Ark of the Covenant

Ethiopia claims that it’s home to the Ark of the Covenant. It’s kept in a church in the city of Aksum that’s so closely guarded, even Indiana Jones would have trouble getting in.

Ethan Hunt wouldn't.

And then he'd be disappointed, because the Ark of the Covenant isn't there. But at least he could add it to his list of "places he went to that he shouldn't ought to have."

6 Like • Comment • View 3 comments

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