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:

Wordsmitty ✍️

about an hour ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

1 Like

🌖 HuntersMoon

about 4 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

1 Like

tj-Merry Mischief Maker

about 23 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

June 15, 2024 at 9:11am

#1072676

My Way or the High Way

From The Guardian, a fairly recent article featured in their "The High Road" section, by that prolific author named Anonymous...

Smoking weed every day makes me less presentable and less productive. I love it

Hey, now, I'm less presentable and less productive, and I don't smoke weed. Well, not often, anyway.

When the pandemic came, I moved back in with my parents in Los Angeles. It was extremely boring.

So are those sentences.

One night we had completely run out of things to do so they decided to go to a local dispensary and pick up.

I don't understand "completely run out of things to do." There's always something to do. Like, maybe, weed.

Smoking with them in the pandemic turned me into a habitual user.

That's right, your parents made you do it.

Now every morning I wake up, I get a fresh pot of coffee brewing and I finish the joint I was smoking last night before bed, which is sitting on my bedside table. When I’ve finished that, I roll another and continue.

Congratulations! You just discovered "Wake and Bake." Literally no one has ever done that before!

Last week my therapist asked me what it’s like being this kind of low-level stoned all day...

Well, there's an obvious way for the therapist to find out firsthand.

Am I addicted to it? Probably, but it works for me and I’m functional.

The first step is to admit you have a problem. The second is to lean into it and decide you like the problem.

Maybe it makes me less motivated, but I don’t really want to be more motivated. I consider wanting to be more productive very lame, like you’ve been cucked by the patriarchy and capitalism.

And that, folks, is a major reason the patriarchy and capitalism have spent the last century or so demonizing cannabis.

I smoke behind the wheel, using my car’s coin tray as an ashtray.

Fuck me, I'm old enough to remember when we used car ashtrays as coin trays.

Personally, I think weed just doesn’t do what alcohol does to you, especially in slow LA traffic. Obviously it is dangerous, but the only road accidents I’ve been in were from before I smoked weed – like driving past an ex-boyfriend’s place and being so in my head that I drove straight into a stationary car.

Okay, look, we all know I like to drink booze. And I generally have no problem with cannabis and would like to see it widely legalized. But driving while impaired is a line I don't cross. Now, sure, you can probably argue, though I don't have the data to back it up, that driving stoned isn't as bad as driving drunk or texting while driving. The problem isn't that you could hurt yourself, but that it's dangerous to other people.

I hate sounding all mud-sticky about this sort of thing, but that's where the author kinda loses my sympathy. "The only road accidents I've been in were from before I smoked weed" could very well be a matter of luck and survivorship bias, like if I said it's perfectly safe to ride in the bed of a pickup truck because I did that when I was a kid and I'm fine.

Last week, my dad called me while I was driving to work and smoking a joint. I made the mistake of picking up and he told me off for driving while I’m high.

Yeah, gonna side with Dad here.

Obviously this means my car smells powerfully of weed, which is not really a problem until I have to use valet parking, but the valets usually find it funny and ask me if they can hotbox it.

Clearly, the author's been lucky enough to never be stopped by cops, either. That's the #1 excuse they give to establish probable cause for a vehicle search, which gives them the opportunity to plant evidence for things that are more clearly illegal, like unregistered guns or meth: "A strong odor of marijuana was noted." (Police reports love to use passive voice.) In the author's defense, though, cops have been known to claim that when they just feel like harassing someone.

I once got kicked out of the parking lot at work for smoking weed and listening to fast jazz too loudly...

Ugh. Jazz? Pfeh. I guess the old scare tactics were right about the connection between weed and jazz. Me, I'd prefer the traditional musical accompaniment: Pink Floyd.

Which, honestly, I prefer to enjoy sober. But to each their own... except, in my opinion, when it comes to driving.

8 Like • Comment • View 2 comments

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