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:

Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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

February 5, 2019 at 1:07am

#951214

A Big Apple a Day

I'm liking this part, we hopped on Amtrak, and headed into NYC after skating last night. Hope you snoozed once you got to the Hilton in Midtown cos, this day is going to be hopping. Did you pay the 750 gps so you can play til dawn cos the Big Apple never sleeps.

https://www.google.com/travel/hotels/Manhattan/place/3041116244787805312?ap=SAE&...

Breakfast at the hotel and we're off. 9am

https://www.tripadvisor.com/AttractionProductReview-g60763-d11854338-9_11_Memori...

11:30 am you're getting on the bus:

https://www.tripadvisor.com/AttractionProductReview-g60763-d11450630-Big_Bus_New...

6:00pm we're doing a helicopter tour of the city:

https://www.tripadvisor.com/AttractionProductReview-g60763-d11447884-Big_Apple_H...

8:00pm we're going to see the Eagles in concert.Got your dancing shoes on cos the night is young and we're going to check out the club scene before we head to the airport. The funkiest story about the nightlife is going to get an added bonus, so surprise me.

No train trip from Philadelphia to NYC can possibly be complete without a mention of the lovely scenery along the way.

Look, I have nothing against New Jersey in general. It did, after all, spawn the greatest musician of all time. And despite what you may have heard, there are some truly nice places in the Garden State.

It's just that none of these places live along the Northeast Corridor.

The Northeast Corridor is the busiest railway route in the US. I can't be arsed to look up the numbers, but it's busy. And when that train gets up around the Newark area, you get treated to a preview of what it'll be like after the Final Plague. Dilapidated factories, sprawling oil refineries, rusty junkyards, oily swamps, dead union bosses, run-down buildings, grafitti-smeared walls.

It's like looking down the ass-crack of America.

Worst of all, even whooshing by at 90 miles an hour does little to mitigate the oppressive stench.

New Jersey is sandwiched between two of the five largest cities in the country. The place is a giant suburb with factories. No wonder they have Issues.

I've been to New York City more times than I can count, and I can count pretty high. I've had family there all my life, as well as the occasional friend. There's no way you can get a feel for NYC in a day, a weekend, even a month. It would take a lifetime to do everything there is to do there. It's almost a world unto itself. I've known people - elderly people - who never set foot outside of the five boroughs. Why? Everything you need is right there.

That said, I'm going to strike out on my own here for a bit. I'd want to stay, for instance, at The New Yorker hotel, just a short block or two from Penn Station.

https://www.newyorkerhotel.com/

It's changed hands a few times, but this is the building where, secluded in Room 3327, Nikola Tesla lived out his final years, communing with pigeons. I made a pilgrimage there, once. My then-wife and I headed up to NYC to see a Leonard Cohen concert, and we stayed at this hotel (staying with my family would have resulted in too many expectations). I hopped onto the elevator and stood in front of that door.

I know I rant a lot here. I expect some people find it tiresome; others, hopefully, find it entertaining. I just have no rants about NYC. Oh, sure, the traffic can suck, but not as bad as other cities. The subways are grimy, but they function. The people have a reputation of being brusque and short-tempered; of course, you can find such people anywhere, but I've always found most New Yorkers to be helpful and friendly as long as you don't block their path. There's crime and corruption, but show me a big city without those things; in NYC, I've seen people walking the sidewalks at night, alone, fearless. I've seen this because at the time, I was walking the streets at night, alone.

And when the sun sets and the city lights up like a constellation... well, if at that moment you don't understand why I'm fond of the place, you probably never will.

Anyway, back to the fantasy tour. I'm going to let y'all young folks like 🌻 thankful pwheeler nano

, queenkissy, SPACE COBWEBS

, and, well, everyone else in this month's 30DBC take over the club. I'm going to head down to the Village and my favorite werewolf-themed pub:

https://www.slaughteredlambpub.com/

Okay, true story about the Slaughtered Lamb. I, and some friends who shall remain nameless because some of them have accounts here, visited that place one kind evening. Let's call them, hm, John, Jack, and Jen (obviously not their real names). We started perusing the menu and I noticed one item that stood out: "Irish Car Bomb - ask me how to get one free."

This, of course, intrigued me. The waitress, who I'll call Jody (again, not her real name) explained that it's a race. You order the ICB, and they send out two of them. Then, you race Jody to drink the thing. If you win, it's free. If she wins, not only do you pay for it, but she gets to whip you three times on the tuchis.

Jack orders an Irish Car Bomb. "Oh," says Jody. "You gonna race me?"

I'm thinking, dude, this chick is a professional. Don't do it unless you enjoy getting whipped. Not that there's anything wrong with that.

"Yep," says Jack.

So Jody brings out the ICBs, sets them up, tells Jen to call go - and they're off.

Jody slugs that thing down in 4.6 microseconds. Jack barely had his tongue wet by the time she slammed the empty glass on the table.

She turns to John. "Can I borrow your belt?"

Grinning, John stands and unbuckles his trouser-strap, hands it to Jody.

"Bend over," she says to Jack. He leans over, hands gripping the back of a chair.

Dude... Jody hit HARD. Three solid whaps, and Jack straightens up, red-faced but stoic.

"Anyone else?" asks Jody. We're all shaking our heads.

"Enjoy your dinner!" and she walks off.

"Well," I says to Jack, "aren't you going to sit down?"

"Nope."

So I'm not ordering any Irish Car Bombs at The Slaughtered Lamb. Still, someone's going to have to come carry me out of there.

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