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:

Turkey DrumStik

about 9 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

October 28, 2018 at 1:10am

#944329

Advice

https://www.thecut.com/2018/10/on-waking-up-early.html

I have some unsolicited work (life?) advice, which is that if you don’t know how to deal with a problem, or a whole host of problems, try getting up obscenely early. Like 5 or even 4 a.m. Just for a little while, at least, like maybe three or four years.

What a coincidence, because I, too, have unsolicited work/life advice, which is that if you don't know how to deal with a problem, drink.

It's easier than getting up early - though not cheaper - and has the added benefit of keeping you from thinking about your problems. And as we all know, if we don't think about our problems, eventually they go away. Things like work, family, and friends, for example. If you think about it, those are the sources of 95% of your problems. (The other 5% usually stem from making stupid decisions, such as not drinking.)

Even if it doesn't work to stop you from thinking about your problems, at the very least it makes you more likely to open up to the bartender about them. Bartenders love to hear about drunk peoples' problems; otherwise, they wouldn't be bartenders. Be sure to tip well. Since you might not be able to compute a proper tip at the end of the evening, just slip her a $20 bill now and then (or, if you're British... well, I can't remember if Brits tip bartenders or not, so come to the US and then tip the bartender.)

As if this weren't enough, drinking will keep you from doing something really douchey like waking up early or starting CrossFit training. If you do happen to wake up early, you'll have a hangover and you'll need to pee. Just remember, don't look into the mirror while you're in the loo. Self-reflection is for sober people.

Meanwhile, you'll find that you're awake, on average, for the same number of hours every day, regardless of when you wake up or when you go to sleep, so don't freaking sweat the whole catching-the-worm thing. After all, as a wise person once noted, "The early bird might catch the worm, but the second mouse gets the cheese."

Oh and hey, quick note - I have to go on an emergency trip to Atlantic City (a good friend of mine just got divorced and he needs to drink), so if I don't post over the next couple of days, that's why.

1 Like • Comment • View 2 comments

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