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 8 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 10 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.

January 31, 2024 at 10:04am

#1063230

Mixed-Up

Before I get into today's article, a quick notice: I'll be participating in "Journalistic Intentions"

[18+] next month, meaning eight of my entries will be themed for that contest. If you have a blog or feel like starting one, it's a good way to spark ideas. (The preceding has been an unpaid public service announcement.)

Once again from Cracked, a beneficial article:

5 Pairs of Extremely Similar Things That You Better Not Mix Up

There are, arguably, too many things in the world. Even if you make it your life’s work to know what everything is, it’s an impossible goal.

Hell, even just trying to get to know every beer is an impossible goal. That doesn't stop me from trying.

Sometimes you might be seeing something that you’re 100 percent sure you’ve identified, and turned out to be plumb wrong.

That's because you used common sense, which is usually misguided.

5. Eastern Coral Snake/Scarlet Kingsnake

If something in nature is frequently enough confused, and with sour enough results, that it earns its own trademark mnemonic device? That’s a pretty good sign that intuition isn’t going to cut it.

I learned this one at a young age, even though neither of these snakes lives in Virginia (yet).

That rhyme, of course, being the famous “Red touches yellow, kill a fellow; red touches black, friend to Jack.” It’s brief, fun and just creative enough to make it kind of hard to remember in an actual emergency. The snake in question is the highly venomous eastern coral snake, and their very similar looking counterpart, the scarlet Kingsnake.

I'm also always confusing the "liquor before beer, never fear; beer before liquor, never sicker" one. Mostly because my primary superpower, besides punning, is that I'm free to ignore such aphorisms. As for snakes, look, they can be beautiful creatures, but I prefer to admire them from a distance.

4. False Morels

I've covered fungus in here before: "Everyone Calls Me Mushroom Because I'm Such A Fun Guy"

. All I have to say about this now is that it's a real morel hazard. Yes, I made that pun in the linked entry, too; shut up.

3. Baking Powder/Baking Soda

Coincidentally, I've covered this one too. Sort of: "Sodium Cool"

2. Fabuloso/Tasty Drinks

Pretty sure this is in the same category as Tide Pods.

You might scoff and say you’d have to be an idiot to ever accidentally drink something that belongs under the sink, but I can tell you from personal experience, even knowing it’s poison, it still looks delicious on a hot day. In big grocery stores, you’d probably get the hint noticing it stocked next to the Windex, but in smaller stores where it might not be that far from the Gatorade? Enough people have made the mistake that warnings have had to be issued, and eventually, the entire labeling was changed to make it more obviously for cleaning and not quaffing.

I consider this to be a self-correcting problem.

1. Your Kid at Chuck E. Cheese

I have never been to a Chuck E. Cheese. I'm pretty sure they were around when I was a kid, but my parents had enough sense not to take me to one. And, of course, being fortunate enough not to have kids myself, I never had a reason to go as an adult. (I have, however, been to Disney World.)

How was I supposed to notice that this one had a different Spider-Man T-shirt on? I haven’t slept more than two hours in five years.

This is why you dress up your kids in a way that makes them unmistakable. You won't ever lose them, and they will never, ever forget it.

I have to admit I'm surprised that the article doesn't include the most important extremely similar thing that you better not mix up: your girlfriend and her twin sister. That shit only turns out well in letters to Penthouse. Just trust me on this.

2 Like • Comment • View 1 comment

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