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!

about 8 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 10 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.

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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 1, 2020 at 12:01am

#986895

Prenatal Parental

So it's July.

For those of you who might be joining us for "30-Day Blogging Challenge ON HIATUS"

[13+]: Hi! I'm Waltz, and welcome to my award-winning blog. Don't be too put off by the math in the header; it's actually just a metaphor.

So it's fortunate that our first prompt for the month lets me write something that's part real, part imaginary.

PROMPT July 1st

Write a letter to your parents from before your birth. Give them advice about how to raise you and give them a heads up about anything they might struggle with when you come into their lives.

Dear Mom and Dad,

I really want you to adopt me so I don't have to grow up in Indiana, raised by someone I presume is an undergrad who got knocked up by some professor. If it helps, they're both obviously supergeniuses. Wait... IQ is a hereditary trait, right?

So I'll say that raising me is going to be (to use a metaphor you might appreciate, Dad) smooth sailing all the way. Yep, no problems at all. Model child.

...You're not buying it, are you?

Well, get used to it. I lie all the time. Usually I call it "fiction writing," except when I try to tell you that it's not my fault (it probably is actually my fault).

Still, truth is, I at least won't be too terribly disappointing. No time in juvie, and the worst trouble I'll get in at school is saying the F word where a teacher could hear me. Well. That's the worst they'll know about. Thanks for teaching me chemistry, by the way. On a related note, I won't do drugs (that you know of), drive drunk, or emulate my biological father by getting some chick pregnant.

I will, however, eternally be the Class Clown. Look, at least I won't be a mime, okay?

Sorry in advance for nearly burning the house down.

I know you're going to worry about me growing up as an only child in a rural area with few friends nearby. Don't. That worked out for the best. I see people terrified of being alone, and you'll teach me that sometimes, it's better. What friends I have will be good ones -- even if you don't always approve of them. They'll teach me things that you can't.

Not about sports, though. I will always suck at sports. Except maybe tennis. But that's okay; the aforementioned "growing up alone" thing will prompt me, above all else, to like what I like, everyone else be damned.

Word of warning: I will, as a kid, get salty about the whole adoption thing. Don't take it personally. It won't be until I'm older that I'll realize it meant that my parents (that's you) really wanted a child, which is more than a most people can ever know for sure. And I never will try to track down my biological parents. There's no need. One family will be enough for me.

Mom, thanks in advance for teaching me how to love the arts and humanities. Dad, same for teaching me about science and technology. Both will serve me well, and not just for the incident with the school's ventilation system that officially never happened and if it did, it's not my fault.

Okay, no, I'm not going to be the perfect child and you're not going to be perfect parents, but we'll get through it.

I'm just glad neither of you is going to be around for the utter shitshow that is 2020. Spoiler: still no interstellar travel, and boy, could we use some of that right about now.

Love,
Your son,
Robert

14 Like • Comment • View 17 comments

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