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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day 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

Nov 14, 2024 at 12:10pm
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.

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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').

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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

January 7, 2019 at 12:44am

#949066

Not Your Daddy's Gilligan

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.

9 Like • Comment • View 6 comments

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