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!

about 2 hours 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

about 4 hours 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.

December 18, 2022 at 12:02am

#1041887

Revisited: "The Only Certainty is Uncertainty"

It's retro time again. Today we're going all the way back to... the beginning of 2021, with "The Only Certainty is Uncertainty"

I probably wouldn't have bothered doing a New Year "looking forward" entry if it weren't a prompt from 30DBC. Or maybe I would have; I don't know. I guess that's part of the "uncertainty" thing.

One thing I hope I will not do: repeat my 2020 "blogging every day" achievement. Because if I do that, it would mean I will have been stuck at home all year again, rather than traveling like I want to.

Well, we know how that turned out: I did manage to travel, albeit only within the US, and I also did a daily blog entry.

Also, the main trip I want to take is to Europe, and last I heard there were still travel restrictions there.

I think those have all been lifted now, but there's still a war going on and no reason to think it won't spill over into NATO and the EU.

On last year's New Year's Day entry, I wrote: "I have some plans, but life has a way of interfering with them." Prescience? Nah, pessimism.

Okay, maybe a little bit of prescience.

A few things, besides travel, that I would like to do this year (meaning 2021)

see movies in the theater

Did that; even reviewed most of 'em.

drink

Definitely did that, although I disappointed myself because I didn't drink as much beer in 21 as I did in 20. My Untapped stats came in for this year a couple of days ago, and I still haven't returned to 2020 levels. So at least I have a goal for 2023.

do the biweekly Zoom meetings for WDC folks

Managed to do that through the end of 2021, but we let it go after that.

listen to music

Yes, but not as much as I would have liked. i mostly do that in the car, and after early July, I no longer had a car.

play computer games

I always seem to manage that, somehow.

blog

As you know.

learn more French and maybe Dutch

Tried Dutch. Found it harder than French. Will try again now that I've gone through all the French lessons.

continue doing Comedy and Fantasy newsletters monthly

Been doing those for 15 years, or thereabouts. No plans to quit soon, though sometimes thinking of a topic is difficult. Even harder to come up with topics I haven't done before.

and attempt to be funny

At that, I was successful. The attempt, that is. Whether I was actually funny or not continues to be a matter of opinion.

So that was my mindset nearly two years ago. We're coming up again on the time of reflection and prediction, all based on the entirely arbitrary changing of the calendar. Will I, again, fall victim to the New Year zeitgeist?

Uncertain.

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