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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/

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Show Recent Comments

10 Most Recent Blog Comments:

tj wanderlust-words-in-motion

about 13 hours ago
In response to "With Pride"

#away!

1 Like

🌖 HuntersMoon

about 19 hours ago
In response to "With Pride"

I'm with you. ### (hashtag pound hastags)

2 Like

Elisa, Stik of Clubs

about 20 hours ago
In response to "Dis Dress Signal"

I think one type of disagreement that gets overlooked but could benefit from this approach is how to enact a shared goal (or express a shared value). Right now, so many disagreements in the spotlight are fairly basic (e.g. USAID should or should not exist). However, if we're going to form alliances to achieve a shared goal (e.g. provide a market for various crops to stabilize prices), we need to be mindful of differences in how these things get done. I worry that people not acknowledging differential priors will hobble potential (and necessary) alliances.

1 Like

Robert Waltz

a day ago
In response to "Dis Dress Signal"

tj wanderlust-words-in-motion

- Ah, but that's what they want you to think.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Dis Dress Signal"

Are you sure it's the lighting? I've heard the "dress" was a government scheme to divide the people and distract us from what's really important. It's all conspiracies, you know!

1 Like

tj wanderlust-words-in-motion

Feb 26, 2025 at 5:11pm
In response to "Cerebral Musings"

I like to think of it as right brained and wrong brained, and many these days are wrong brained.

1 Like

tj wanderlust-words-in-motion

Feb 25, 2025 at 4:32pm
In response to "Solitary"

Having five brothers and one sister, I often seen less family stress in friends that were an only child.

1 Like

tj wanderlust-words-in-motion

Feb 24, 2025 at 6:17pm
In response to "Mystery"

#tiktokgirl: octothorpe, number, and as you indicated poundtiktokgirls. That's the problem with "the style these days", they distort all the coolness of the past styles.

1 Like

tj wanderlust-words-in-motion

Feb 23, 2025 at 4:32pm
In response to "Revisited: "Forgive Me, For I Have Zinned""

My oldest son, while in college, would buy it and mix it with Kool-Aid when he had friends over.

2 Like

Allan Charles 🐾

Feb 23, 2025 at 12:03pm
In response to "Revisited: "Forgive Me, For I Have Zinned""

I find White Zinfandel to be disgusting. Defining it as the wine equivalent to American cheese is a great comparison.

At my job, we only sold a cheap house wine for white zin, and when people ordered it I had to try to restrain my facial muscles from giving stank face.

2 Like

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