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.

July 22, 2019 at 12:03am

#962976

Putting the Vice in Advice

Share three pieces of advice you’ve received through your life that you wish you had heard earlier.

Advice? I'm more into vice.

It's not that people didn't give me this advice when I was younger; it's more that I was so sure I would be the exception that I didn't fucking listen. Which I guess is the same thing as "I wish I'd heard the advice."

1. It's okay to be alone.

Turns out it's better to be alone than to be with someone who's wrong for you. Who knew? Well... literally everybody, except me of course.

On the other hand, I've known people who were deathly afraid of being alone. I suppose that advice wouldn't have worked out for them, but it seems that I'm mostly introverted anyway, so being with other people isn't a high priority for me. Sure, I need it sometimes, but usually a bartender is enough.

2. Exercise daily.

I'm sure this seems obvious to people. Hell, it's obvious to me, now. But I thought I could break all the rules, again, and I ended up playing catch-up after some medical issues. I always figured, what's the point of living longer if you're just having to spend all that extra time exercising? I still believe that, in theory, but it turns out there are more immediate benefits, not just potentially longer life.

3. Budget.

My parents did a fair job talking to me about money, but it still wasn't enough. I was stupid about money matters for way too long. It's not like these things are taught in schools; I had to figure it all out on my own. When I did, my epiphany was like, "Huh. My parents were right." Fortunately (or unfortunately, depending on how you look at these things), by that time my mom was gone and my dad wasn't in any position to say "I told you so," or anything else coherent for that matter.

There's also a great deal of advice that you hear that's utter bullshit. Or, to be fair, it's bullshit for you; maybe not so much for the person offering it. The real question, then, is: how do you tell good advice from bad?

Unfortunately, the answer to that is, "Make your own mistakes." I doubt I'd have learned anything if I hadn't come to these conclusions myself. I'm stubborn like that. So here's my advice:

Don't take advice.

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