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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 13 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 15 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.

May 10, 2020 at 4:06am

#983209

Myth of Family

GAAAAH! I should have known something like this was coming, and skipped this month.

PROMPT May 10th

The prompt today is very simple: Write about the person you call Mom.

Every year starting, oh, around Passover, my inbox starts getting spammed with Mother's Day advertisements. "Gifts Mom Will Love!" "Treat Your Mom To This Shiny Thing!" "Make Mom Happy With This One Weird Trick!"

Now, I'm not against getting emails from companies I do business with, even if they're ads, but I wish Gmail had a "time out" function where I could send mail by certain senders into the Spam folder between, say, April 1 and May 20, and I'd do that with any merchant who uses the words "mom" or "mother."

It's not that I object to the made-up holiday itself. I mean, all holidays are made-up. Yes, that one. That one, too. Especially that one with the jingling bells and ho-ho-hos. Some were just made up earlier than others. But look, even the woman who thought up Mother's Day in the first place tried to make it go away

because it became commercialized.

Still, it's not the commercialization that annoys me. Start anything in the US, and it will become commercialized, just as sure as the sun rises in the east and gives you cancer if you're out in it for more than 30 seconds.

Some mothers are simply not worthy of worship on this fine day. Some of them are so toxic, so venomous, that you're better off just cutting them loose. Oh, I know, I know, "family above all and she's your MOTHER how DARE you," well, bullshit. If your maternal figure tears you down, undermines you, guilt-trips you, ridicules your aspirations, insults your dog, tries to run your life, or otherwise destroys your self-esteem, cut her loose. Mother's Day would be an especially good time to do this. Oh, sure, maybe she shat you out so she'd have someone to take care of her in her old age, but listen: you owe her nothing if she's not going to take care of you.

Eh, that doesn't apply to me either. But I have friends who complain about their mothers' bullshit, and yet still worship them. The myth of family is so ingrained in society that they just don't see there's a way out. You'll divorce your spouse in a heartbeat, even though you chose them, but separating from your mother feels like shitting on God, the American Flag, and a stack of $100 bills all at the same time. I can only imagine it's worse in cultures with an even stronger myth of family.

I have one friend who did it, "divorced" her mother. The lady is legit psycho, and my friend just couldn't deal with her anymore. But she still feels guilty about it sometimes, I think, and especially in May.

This all of course goes for dads, too, and if it were June that's what I'd be ranting about. But it's not. It's May. Besides, somehow it's more acceptable to kick your dad out of your life than your mom, maybe because so many fathers "go out for cigarettes" and never come back.

I don't mean you should ignore your mom if she simply votes the other way from you in elections, or gives unsolicited advice, or shows up unexpectedly. But despite what everything in society screams at you all the time, there are situations where you're better off without her.

My mom wasn't terrible, and I helped make sure she was taken care of in her old age, and I was looking into her eyes as she died, 21 years ago. I'm done with moms.

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