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Thursday, Mar. 6, 2025

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj wanderlust-words-in-motion

about 9 hours ago
In response to "Shhhhhhh"

I may have a slight allergy to delusional people; they give me a headache.

1 Like

Wordsmitty ✍️

about 10 hours ago
In response to "Shhhhhhh"

I drove by that several decades back either coming or going to a vacation somewhere beyond. It's so strict that even birds couldn't tweet there. (someone had to say it)

2 Like

BIG BAD WOLF is Merry

about 13 hours ago
In response to "Shhhhhhh"

Always someone complaining about something, annoyingly.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Now, That's Using Your Noodle"

I wish my ex-mother-in-law could have read this, her idea of perfect pasta was when it went fully limp and flat! Of course, even if this was presented to her, it wouldn't help, another of her cherished traits was you couldn't tell her anything.

1 Like

Annette

a day ago
In response to "Now, That's Using Your Noodle"

My French grandmother had zero advanced degrees in anything, but every single meal she has cooked in her life would put these scientists as well as every single Michelin starred chef back into his little corner.

I bet that there were and still are billions of women making daily delicious dishes without needing a PhD.

These men made it their profession to play with food, only to come to the conclusion that they need to shut up and give compliments to the real chefs of the world.

I know there is the occasional woman who doesn't care for cooking. But they also don't go around meddling with others' cooking skills.

2 Like

Adhere - Definitely Writing

a day ago
In response to "Now, That's Using Your Noodle"

Your research trip sounds important - if you get funding I'd volunteer to come along as a research assistant - I think we should definitely look at the 'perfect' wines to accompany pasta dishes - which would take simply ages to determine.

3 Like

tj wanderlust-words-in-motion

Mar 4, 2025 at 3:41pm
In response to "Stress Marks"

I agree, there are many ways to indicate stress in writing; there's no reason to get stressed over it. Just stay constant or you may stress out your readers!

BIG BAD WOLF is Merry

Mar 4, 2025 at 10:51am
In response to "Stress Marks"

There's always something that one can do.

tj wanderlust-words-in-motion

Mar 3, 2025 at 4:36pm
In response to "Life As We Don't Know It"

There's probably a sign at the edge of the Milky-Way that reads, "Caution, enter at your own risk!"

1 Like

Annette

Mar 2, 2025 at 2:18pm
In response to "Revisited: "Real Men of Genius""

My second son was born at almost the exact same time as one of my uncles died. When second son was a baby, we looked out for signs whether there was some reincarnation going on.

If there was, then he is a great example of nurture versus nature. Where my uncle was creative, sensitive, and mentally destroyed by the time he was a teen, my son's creative side is thriving, he has turned his sensitive nature into a passion for anthropology, and he knows he is loved unconditionally.

Maybe reincarnation is simply one generation deciding to put a stopper on past generations' bad habits.

1 Like

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