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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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').

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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 19, 2019 at 12:05am

#970019

Getting the Lead Out

PROMPT November 19th

What characteristics do you admire in a leader? Is there or was there a time in your life when you took on a leadership role? Research different leadership styles and describe which style you would most like to follow. Which style are you? When you are in a leadership position, do you exemplify the qualities you admire in a good leader?

A good leader leads by example.

I am a Bad Example. I even printed up "business" cards with my name followed by "Bad Example." I also had such phrases as "Millionaire Playboy" and "Evil Genius."

Basically, I don't want to be a leader. I don't like it. The benefits don't outweigh the constrictions, for me. I admire those people who can do it, and maybe they're more appreciative of the admiration of others than I am (thus changing the cost/benefit analysis). But there's one thing I hate more than being a leader, and that's being a follower.

Of course, I've done both, especially in my engineering career - though when I ran a business, it was with a partner, so a lot of the "leadership" things were shared. But I tried to set a good example for employees by following the same schedule as, or sometimes a more hectic one, than I expected of our employees. "Never expect anyone to do what you won't." I didn't have that in a boss; all my previous employers thought that it was just fine to expect us to work 8 to 5 while they could show up at 10 and leave at 3. Just to use one example. Of the two modes, I decided I preferred being in charge - not for any perqs (the higher salary was nice, though), but just because when I make the rules they are, by definition, not idiotic. Perhaps my employees felt differently; I don't know. I suppose not knowing makes me a bad leader after all. In any case, preferring it doesn't mean I enjoyed it.

Fortunately, life isn't binary, and I choose Option C: going my own way. It's enough to be responsible for my own situation, and I'm not always so good at even that.

There are, of course, other qualities that define good leadership. The ability to delegate is one. And I don't just mean foisting off work on just anyone, but matching peoples' strengths to the tasks at hand. I wouldn't assign an artistic type something that's math-heavy, or the other way around. Knowing what people are good at is important. Knowing what they could be good at, given a chance, well, that's even better, and I wish I were better at it.

Another thing I'm terrible at is motivating people. I like it when people motivate themselves. Any attempts I make in that direction always seem hollow to me. But I think good leaders find ways to motivate their team, though how they do it might as well be sorcery for all I understand it.

Anyway, yeah, this is kind of rambling, but the bottom line is: don't look to me to set examples, unless you enjoy drinking at bars.

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