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:

Brandiwyn🎶

a day ago
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').

1 Like

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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

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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