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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 9 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 11 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.

June 11, 2021 at 12:03am

#1011656

Useful

Just a little fun today.

The Forgotten Uses of 8 Everyday Objects

Some of the products we use daily have functions most of us are completely unaware of.

Yeah, like my mobile phone. Did you know you could use it as a phone?

1. THE TINY “EXTRA” POCKET ON YOUR JEANS

You’ve probably noticed that some of your jeans have a small pocket located in one of the front pockets. Many people think the tiny addition is meant to keep coins from jingling around in the larger pocket, but according to Levi’s, they created it to provide extra protection for pocket watches.

And no one has pocket watches anymore, except for truly eccentric attention-whores and, well, me, but mine's a family heirloom locked up somewhere safe.

Which means that jeans outlived pocket watches. There's something to be said about fashion that doesn't go out of style.

2. THE HOLE IN YOUR POT HANDLE

Most pots and many pans are designed with a small hole at the end of the handle. While they make for an easy way to hang your pots and pans when they're not in use, they were also designed with another purpose in mind: as a way to hold your spoon or spatula in place over the pot itself, and save yourself from making a mess of your stovetop.

Yeah, I've seen this idea floating around for a while. I call bullshit. I tried using the ones on my pans that way and ended up making a mess of my stovetop.

They are, however, indeed convenient for hanging the buggers.

3. THE LOOP ON THE BACK OF YOUR DRESS SHIRTS

If you look below the collar and between the shoulders on the back of many men’s dress shirts, you may spot a little loop. Though most men probably don’t use it for its intended purpose—at least, not often—it's there to provide a convenient way to hang up the shirt when a hanger is unavailable.

Whaaaa? That's what chairs are for. And as kids, we had rude names for these loops. "Fruit loop" was the least offensive of the bunch.

4. THE GLOVE COMPARTMENT

More like the user manual compartment.

5. THE HOLES IN YOUR BOX OF ALUMINUM FOIL

If you've ever studied a box of aluminum foil or cling wrap, you may have noticed that there are little indentations that, once pushed in, create small holes on either end of the box. Look a little closer and the reason for these holes is printed right on the box: "Press to lock roll."

I used to be one of those people who would read the fine print on anything, lest I miss something important. So yeah, I knew this. But when I try to use these tabs for their intended purpose, it's a bigger pain in the ass than if I don't.

6. THE DRAWER UNDER YOUR OVEN

If you keep cookie sheets, cupcake pans, and pancake griddles in that narrow little drawer under your oven, you’re in good company—so does most of the rest of the world.

Because that's what it's for and I refuse to revise my knowledge to fit any so-called "facts" about it.

7. THE ADDITIONAL HOLES ON YOUR CONVERSE SNEAKERS

They're talking about the air holes, but back when I had Converse sneakers, you know, when they cost like five bucks instead of 1500, I had all kinds of additional holes in them, none of which were intended by the manufacturer.

8. THE LOOP ON THE SIDE OF YOUR CARPENTER JEANS

THEY'RE CARPENTER JEANS WHAT THE HELL DO YOU THINK THAT'S FOR?

Also, did you notice that all of these are about holes? If I were a shrink, I'd have a field day with that.

Anyway, like I said, just a bit of fun, but I can't leave this without doing my quick review of Cruella, which I saw yesterday.

One-Sentence Movie Review: Cruella

I probably wouldn't have appreciated this movie as much if I hadn't spent the time, earlier this week, to watch both the original Dalmatians cartoon and its live-action remake; as it is, while my expectations were fairly low, it turned out to be a fun movie about the perils of working in the cutthroat fashion industry -- and maybe a few other, minor themes like betrayal and revenge -- consequently, as much as I desperately wanted to describe the movie as "spotty" to make a really, really bad Dalmatian pun, I cannot, because it's pretty tight, just like the outfits it features.

Rating: 4.5/5 (but probably more like 3.5 if you haven't seen or don't remember 101 Dalmatians)

8 Like • Comment • View 3 comments

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