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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 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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