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!

a day 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

a day 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.

November 6, 2019 at 12:06am

#969085

Oy, This Dreck Again

PROMPT November 6th

I have another link for you all today:

http://www.wmfc.org/uploads/GenerationalDifferencesChart.pdf

What parts of the chart did you find to be accurate and which did you find issue with? Anything you related strongly to? Is a chart like this useful, or does it rely too heavily on stereotypes?

I've said this before and I haven't run into anything that has changed my opinion: "generations" are utter bullshit; people are born, live and die on a continuum; and attempts to pigeonhole us are about as useful and accurate as star charts and Facebook quizzes.

Also, as Barack Obama (misspelled on the chart) is listed as a GenXer when by its own reckoning he's a Boomer, having been born (IN THE US FOR FUCK'S SAKE) in 1961. Given that simple error (compounded by the typo), I can't trust anything the chart says. And further yet, by my calculations it's a good 11-12 years out of date now.

And what the hell is it with the two date ranges for Millennials? Can't that generation do anything right? (KIDDING I'M KIDDING JEEZE)

Again, I've run through this argument before, but for newcomers: I was born in 1966. That would put me in GenX, along with people born (per the chart) in 1980. So they'd lump me in with someone from 1980, 14 years distant, but not from 1964, 2 years separated? How about twins born on the cusp of 1964-65? Theoretically, one could be a Boomer and his or her little sibling (by all of three minutes) could be an Xer. That could make Thanksgivings way fun as the older sibling could throw "kids these days" shade at the younger one.

It's really remarkable how much work has gone into the preparation of this nonsense chart, without even the fun math involved in astrology, or the years of college needed to come up with a Myers-Briggs analysis.

The whole "generations" thing was developed, I'm pretty sure, as a tool for marketers as a way to target people for manipulation. This is seen nakedly in the stuff at the very bottom of the chart, which admittedly I skimmed down to.

I'm not saying everything in it is wrong, of course - after all, Xers are "skeptical" and "cynical." Hey, spot on there. Stopped clock and all that.

So of course I tried to track down where the pdf came from. The webpage corresponding to the domain in the pdf's URL (try telling THAT to someone from 1965) is the West Midland Family Center, out of Michigan - hence, one supposes, the focus on the various cohorts' work ethics and "fundraising tips."

But that gives me the opportunity to point out a rule that has never led me astray in all the years I've followed it. To wit:

Never trust an organization with the word "Family" in the name.

Inevitably, they are run by people who are appalled at the idea that someone, somewhere, who is not a child, is having fun, and will work very, very hard to stop that nonsense immediately.

Now, I don't know... I haven't clicked around that particular organization's website very much. Could be they're an exception. I wouldn't bet the farm on it, though. (I actually do own a farm, by the way. That's not just an expression for me.)

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