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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 9 hours 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

about 10 hours ago
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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

February 28, 2022 at 12:04am

#1027582

Let Us Dance in Style, Let Us Dance for a While

Hey look, a midnight posting. Helps that it's only 9pm here.

One oddity (of many) about the L.A. area is the prevalence of astronomy observatories here. By my count, there are at least three: Mount Wilson (from yesterday's blog), Palomar (which I understand is currently closed) and Griffith, which is kinda sorta near some place called Hollywood.

That's where we went yesterday. Griffith, that is, not Hollywood.

As an aside, y'all know I love movies. So, probably, you'd think I'd be interested in seeing the movie part of L.A. But I'm not. I mean, I wouldn't turn it down or anything, but it's way too touristy and kitschy for me. I'm happy to watch the movies back on the other coast and then do other stuff in L.A., which is, after all, a really large area with lots of other stuff to do, including the reason I travel in the first place (breweries).

Still, I couldn't resist getting lots of pictures of the famous HOLLYWOOD sign from various points in Griffith Park.

But the cool thing, to me, was the observatory itself. I don't think they do actual science there anymore, but the history is impressive, as is the building itself. They've converted it into a museum.

One thing that struck me was seeing just how goddamned busy it was. Crowded, even. This usually annoys me; crowds just get in my way, even disregarding the whole germ-spreading thing. But then I thought about it for half a second (I hadn't started drinking yet, or it would have taken two or three seconds), and realized: here are people jamming into a monument to SCIENCE on a Sunday afternoon. Some of them might even learn some shit. Some of them might even decide to learn more shit later. If there is a later...

After Griffith, then we went to breweries, which were of varying quality but overall had delicious beer.

Consequently, I'm just drunk enough to post this, after finally receiving yesterday's damage report upon returning to my hotel room.

Let us dance in style, let us dance for a while
Heaven can wait, we're only watching the skies
Hoping for the best but expecting the worst
Are they gonna drop the bomb or not?

Let us die young or let us live forever
We don't have the power but we never say never
Sitting in a sandpit, life is a short trip
The music's for the sad men

Can you imagine when this race is won
Turn our golden faces into the sun
Praising our leaders, we're getting in tune
The music's played by the, the mad men

Forever young, I want to be forever young
Do you really want to live forever, forever and ever?
Forever young, I want to be forever young
Do you really want to live forever? Forever young

Some are like water, some are like the heat
Some are a melody and some are the beat
Sooner or later, they all will be gone
Why don't we stay young?

It's so hard to get old without a cause
I don't want to perish like a fading horse
Youth's like diamonds in the sun
And diamonds are forever

So many adventures couldn't happen today
So many songs we forgot to play
So many dreams swinging out of the blue
If we let them come true

Forever young, I want to be forever young
Do you really want to live forever, forever and ever?
Forever young, I want to be forever young
Do you really want to live forever, forever and ever?

Forever young, I want to be forever young
Do you really want to live forever?

9 Like • Comment • View 2 comments

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