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:

Write_Mikey_Write!

about 22 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 24 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.

January 16, 2020 at 12:12am

#973487

Invincible

PROMPT January 16th

What are you waiting for?

There are so many ways to answer this question, both light and heavy, so I look forward to reading where you go with it!

Death.

Now that I've gotten that out of the way...

I'm one of those people - yes, those people - who usually answers rhetorical questions literally. And "What are you waiting for?" is normally a rhetorical question. "Will you take the trash out, dear?" "Sure." "...Well? What are you waiting for?" "The sweet release of the Apocalypse."

It's not that I don't recognize rhetorical questions; it's that I hate them and respond with snark. Well, sometimes I legitimately don't recognize them. It's the same for me with sarcasm.

When it's not a rhetorical question, it implies a call to action. "You say you want to go to Belgium. Your passport is up to date and you have money. What are you waiting for?"

Well, for one thing, Not January. I hate being cold, and Belgium is kinda... north.

For another, I still have a reluctance to travel to a foreign country alone. I mean, I did it with the UK, but there, I have a rudimentary grasp of the language, and also I was visiting friends.

But mostly, it implies that I should be doing something other than what I'm doing right now, but whatever it is I'm doing right now is generally what I really want to be doing. In the battle between "should" and "want," "want" wins every time. That's just the way I am. My trick has always been to work toward wanting to do the things I should be doing, and it sometimes works (as with exercise), provided someone else doesn't muck things up by trying to noodge

me into doing it.

(First known use of noodge, 1967? That doesn't make any sense. My mother had a meager knowledge of Yiddish that she got from her mother, and for Grandma, it was her first language. By 1967, Mom knew all the Yiddish she was ever going to know, and noodge was one of the words. I know this because every time I asked for something more than once, I got "Stop noodging me!")

Really, I'm not waiting for anything important. I have a few set plans: there's a wine tasting tomorrow, of Bordeaux wines hosted by an actual French person from France...

...and then next Tuesday the local cinema / drafthouse is going to have a Big Lebowski movie party. I resemble The Dude, so it should be interesting. Also, next Saturday is a winter beer festival, so my Sunday morning blog should be amusing, from a certain point of view. You can wait for that if you want.

But it's not like I'm sitting here just waiting around for these events. I have Netflix shows to binge.

This bloody road remains a mystery
This sudden darkness fills the air
What are we waiting for?
Won't anybody help us?
What are we waiting for?

We can't afford to be innocent
Stand up and face the enemy
It's a do or die situation
We will be invincible

7 Like • Comment • View 6 comments

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