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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.




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January 7, 2019 at 12:44am
January 7, 2019 at 12:44am
#949066
You and several friends are marooned on a desert island. Everyone is looking to you to lead. What are your first actions?

Panting from the long swim, we all flopped onto the beach like turtles.

After catching my breath, I surveyed the survivors. As the obvious leader, the others all looked to me for direction.

"Okay," I said, getting to my feet. As I brushed the sand from my ruined trousers, I addressed the small group. "Priorities. Mike."

"Sir?"

"This is obviously a desert island. Find the stash of rum."

"Yes, sir!" Mike jumped upright and began jogging along the stretch of golden sand, head searching side to side.

"Now, the rest of you. As unexpected as this was, we did come prepared. Everyone has their five 'stranded on a desert island' CDs?"

"Yep." "Uh huh." "Right here, boss." "Of course." The other six simply nodded. One by one, they struggled to standing positions.

"Sharon?"

Pulling some jewel cases from a pouch, Sharon read the titles. "Led Zeppelin, you know, the fourth album. Counting Crows, August and Everything After..."

I cut her off with a gesture. "Good enough. You're the cook."

"Excellent," she smiled.

"Kenneth?"

"Eagles, Hotel California. Meat Loaf, Bat out of Hell. Jethro Tull, Songs from the Wood..."

"Yep," I interrupted. "You're in charge of shelter."

"Will do." He loped off toward the treeline.

"Ellen?"

"Um... Coldplay, X&Y. Dave Matthews Band, Everyday. Nickelback-"

"Stop," I commanded. "Ugh. Ellen, you're dinner."

"But I-"

"Report to Sharon."

"Aw."

"Now, where was I? Steve."

Steve opened his mouth to speak, but at that moment Mike returned, lugging an iron-bound chest on one shoulder, sand still clinging to its bottom half. "Found the rum!" he announced.

"Okay, never mind. We'll go over discs later."

Mike started distributing bottles.

Ann turned to me.

"Um, Robert?"

"Yeah?"

"Did, um... did anyone bring a CD player?"

They all looked at me.

"D'oh," I said.


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