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:

tj-Merry Mischief Maker

about 21 hours 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

a day ago
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

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

August 19, 2024 at 10:05am

#1075462

List-erine

This bit from The Guardian is a couple of years old, but that's okay. Just remember it's British.

100 ways to slightly improve your life without really trying

If #1 isn't "stop reading fluffy internet advice articles," it fails.

1 Exercise on a Monday night (nothing fun happens on a Monday night).

Oh. Oh, no. Shit. It's going to be one of those articles.

3 Tip: the quickest supermarket queue is always behind the fullest trolley (greeting, paying and packing take longer than you think).

Except when the person pushing that cart is the kind who still pays by check, and goshdarnit, I know that checkbook's in here somewhere, hang on...

5 Consider going down to four days a week. It’s likely a disproportionate amount of your fifth day’s work is taxed anyway, so you’ll lose way less than a fifth of your take-home pay.

Taxes don't work like that in the US, and I wasn't aware they worked like that in the UK.

10 Always bring ice to house parties (there’s never enough).

Be sure to leave it in the living room, preferably on the couch.

12 Sharpen your knives.

Damn, I hate that there's one I absolutely agree with.

14 Buy a cheap blender and use it to finely chop onions (it saves on time and tears).

Sure, if you want onion purée. And an extra mess to clean up. Also, what's the point of having finely-sharpened knives if you can't use them to chop an onion quickly?

16 Set aside 10 minutes a day to do something you really enjoy – be it reading a book or playing Halo.

No. Set aside 23 hours and 50 minutes a day to do what you really enjoy, and devote the rest of the time to work.

23 It might sound obvious, but a pint of water before bed after a big night avoids a clanger of a hanger.

True, but if you're drunk enough, you won't wake up when that pint has been processed, if you know what I mean.

29 Eat meat once a week, max. Ideally less.

I believe the expression is, "Sod off, wanker."

39 Send postcards from your holidays. Send them even if you’re not on holiday.

This has the added benefit of pruning your friend list, which in turn means fewer holiday gifts to purchase and fewer birthdays to remember.

41 Buy a plant. Think you’ll kill it? Buy a fake one.

I don't think I'll kill it; I know I'll kill it. Yes, even if it's a fake one.

42 Don’t have Twitter on your phone.

This one's three words too long.

46 Read a poem every day.

Technically, limericks are poems.

49 Buy in person!

Fuck off!

51 If something in the world is making you angry, write (politely) to your MP – they will read it.

This sentence is the only one on the list that I find impossible to translate from British to English. I mean, sure, our congresscritters are the rough equivalent of British MPs, but it's the last phrase after the emdash that broke my brain.

56 Call an old friend out of the blue.

Drunk-dial an ex.

62 Go to bed earlier – but don’t take your phone with you.

Why? If you're getting the same amount of sleep either way.

65 Instead of buying a morning coffee, set up a daily transfer of £2 from a current into a savings account and forget about it. Use it to treat yourself to something different later.

How can I do that if I've forgotten about it?

72 Always use freshly ground pepper.

Dammit, how dare they put in another one I'd have to agree with!

76 Ditch the plastic cartons and find a milkman – The Modern Milkman has a comprehensive list.

This is some sort of euphemism, right?

89 Politely decline invitations if you don’t want to go.
90 If you do go, have an exit strategy (can we recommend a French exit, where you slip out unseen).

Pretty sure that's known in France as la sortie anglaise.

93 Do that one thing you’ve been putting off.

Then find something else to put off.

100 For instant cheer, wear yellow.

Look at the stars. Look how they shine for you. And everything you do.

4 Like • Comment • View 2 comments

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