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.

September 8, 2019 at 12:09am

#965799

Leadershit

PROMPT September 8th

Prompt today is submitted by Elle - on hiatus

!

What do you think makes a good leader? Share an example of a good leader from your life (or alternatively, a poor leader who taught you what not to do).

It helps to have rolled a high Charisma score.

Aside from that, well, I think a good leader motivates, encourages, kicks butt when necessary, knows when kicking butt is necessary, reads people, understands a person's strengths and weaknesses, and, probably above all, leads by example.

I worked with a guy for 15 years who mentored me in engineering. He'd answer questions, show me efficient ways to do things, and help keep me focused. We had somewhat different skill sets, at least starting out - I was always the computer nerd, while he was more old-fashioned with a pocket calculator - but gradually we picked up each other's skills.

After those 15 years, he left to start his own company and poached me from our old one; we were both dissatisfied with the way the boss was running things. A bunch of people left all at once. So I started working for him directly, and that's when things started going to shit. He'd emulate our former boss by coming in late, taking long lunches, leaving early, and generally fobbing off most of the work on me. Not a great example. This was especially disappointing to me because, while we were never friends outside of work, I thought we had an understanding. When you know someone for 15 years, you think you actually know them, but things change, I guess.

After a couple of years of this, I left with another of his employees to start our own firm. Karma can be a bitch. At that point, I was still doing all the engineering work (my partner was in another discipline), but at least I was reaping the rewards as well.

My business partner and I never had more than three employees, but I like to think we were better to them than my bosses had been to me. I don't know; I don't have much to compare to. At least I tried to lead by example.

These days, I'm happy being responsible for no one but me and my cats. Not that I don't have other responsibilities, but they're hardly onerous.

I don't know what happened to my former co-worker turned boss, by the way. I hope he ended up successful. I don't hold a grudge; I just couldn't be in that situation any more.

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