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:

Write_Mikey_Write!

about 10 hours 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

about 12 hours 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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 4, 2022 at 12:01am

#1031888

Oh, Canada...

Today, we go back to Cracked for an article from December about America's Hat.

15 Canadian Words Every American Should Know

And I don't think they're talking about "hockey" or all the extra "u"s in their words.

Either because you're planning a trip to the Great White North, or you just want to be prepared in case you ever run into Keanu Reeves and don't want to look like an idiot, it's not a bad idea to know some Canadian words.

You know, it wasn't even on my radar that Keanu Reeves was Canadian. And I'm usually aware of these things, whether I want to be or not. Well. It's not like he ever chugged maple syrup in any of his movies that I've seen.

As usual, it's a countdown list, and as there are 15 of them, I'm going to choose just a few highlights.

13. “Toque” Basically Means “Beanie”

Yeah, I knew this, thanks to Rick Moranis and Dave Thomas (Canadians). But I rarely have occasion to use the word, because I live in a relatively warm country.

In the U.S., there are Beanies; in Canada, you have "Toques" -- pronounced like the family of Hobbits.

Is it, though? I've always heard it pronounced with a long oo, like in mook or boob, and I thought you pronounced the Hobbit name "Took" like "took." Looking at the word, though, you can't tell: it could be tuck or took or tooook or tock. And you can't even go to the original French for answers, because they call a beanie "un bonnet." Pronounced bonAY of course.

So, like, JayNaNoOhNo or any other Canadians reading this... which is it? Or maybe it's regional.

10. A “Snowbird” is Less Fun Than it Sounds

"Snowbird" is a song popularized by Canadian music legend Anne Murray -- but more commonly it's used, not to identify wintery fowl, but to describe the senior citizens who head to Southern U.S. states such as Florida during the colder months...

Hey, we call 'em that, too. When we're being polite.

6. A "Double-Double" is Coffee With Two Creams and Two Sugars

In the U.S., you might know it as a basketball term or a precarious sexual position (we're guessing), but it means a coffee with two creams and two sugars for Canadians.

Hey, Canadians, remember this next time you're thinking of ragging on the drink preferences of your neighbors to the south.

4. “Parkade” is Just a Parking Garage

The word "parkade" refers to a "multi-level parking garage" and appears to date back to Edmonton, Alberta in the 1950s. It's a pleasant word we should frankly all adopt.

I gotta agree with Cracked here.

3. “Pop” Means “Soda”

If you hear a Canadian ask for a "pop," they're not necessarily asking someone to hand over their elderly father. Most likely, they want a soda.

Many electrons have been wasted on discussing the regional variations in what people call carbonated soft drinks. People have actually gotten grants to study that shit. "Pop," as you probably already know, isn't unique to Canada; a huge chunk of the US

calls it "pop" also.

Incidentally, here's a map

of the US, county by county, with visualized results of this important linguistic analysis.

For the record, I call it "soda."

1. A "Two-Four" Means You're About to Get Drunk on Mediocre Beer

A case of twenty-four bottles of beer is often referred to as a "two-four" – and just think of all the extra time you'll have to get drunk thanks to the valuable seconds you saved by omitting that extra syllable.

I suppose we should be grateful they don't call it a deux-quatre. Though this is something I'll never need to know, because I don't drink beer that's sold in cases.

So, like I said, there are a few more at the link, if you care to become bilingual and learn some Canadian

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