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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Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

about 7 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!

Nov 14, 2024 at 2:04pm
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.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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').

1 Like

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

November 22, 2018 at 12:06am

#946002

Thanksgiving Day

In honor of Thanksgiving, five things I'm grateful for:

1) Beer.
2) Wine.
3) Scotch.
4) Gin.
5) Tequila.

Cheating? Okay, yeah, that's cheating. Let's condense those into one category and try again.

1) Alcohol.
2) Hookers.
3) Drugs.
4) Porn.
5) Gambling.

...nah, that won't play very well with the test audiences. How about one more try, this time serious.

1) Alcohol. (Yeah, this one's staying on the list.)
2) The internet. (I mean, where else can I meet people from pretty much everywhere? Besides Las Vegas or New York.)
3) Modern medicine. (Because of it, I'm still alive to make lists.)
4) Cats. (Dogs are fine, but too much work. Cats appeal to my lazy nature.)
5) Money. (Anyone who says the best things in life are free has never had a really good single-malt scotch.)

And in honor of the Thanksgiving holiday, I have composed a poem, the first one I've attempted in a long while. It's inspired by my second attempt at a list, above. It's called...

Alcohol, Hookers, and Blow

There are many things to be thankful about
In a life of contentment and joy.
But on this fair Thursday, I think I will go
With alcohol, hookers, and blow.

Weed is just fine, and legalized now,
But meth is a dangerous drug.
So I'll stick with the stuff I already know,
Like alcohol, hookers, and blow.

Our vices in life can be curious ones,
And sometimes the secrets we keep,
So I'll leave this out here and put on a show
With alcohol, hookers, and blow.

Beer is terrific and wine is okay,
While gin is my poison of choice
For when I get ready to spend all my dough
On alcohol, hookers, and blow.

From Reno to Jersey the gamblers play
In casinos and Indian bars,
But really, the answer is hitting the flow
With alcohol, hookers, and blow.

Life is uncertain, could end anytime
And death is a permanent state.
So I thank the gods and the folks down below
For alcohol, hookers, and blow.

4 Like • Comment • View 4 comments

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