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 10 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 12 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').

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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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

February 25, 2024 at 9:53am

#1064849

Revisited: "Cheese? What Kind of Cheese? I Want Brie"

In September of 2020, WDC celebrated 20 years of online activity, and my account reached its 16th anniversary. Today's throwback reminded me of this, because it was from the beginning of that month: "Cheese? What Kind of Cheese? I Want Brie"

Hm. Another WDC birthday week. That means I'll be 16 soon.

Obviously, that means that, in about six months, I'll be turning 20. Damn, I can't wait until my account can legally drink. No, I mean I literally can't wait; I do it anyway.

The linked entry was a response to a prompt from "30-Day Blogging Challenge ON HIATUS"

[13+], which I miss, but I have some idea of the amount of work involved, which makes me shudder to think about. The prompt was, in part: "I know this is cheesy, but I have to do it... In your entry today, write about what you love about Writing.Com."

Hence the "cheese" reference in the title.

You know, my hesitation on prompts like this is not that it's cheesy. I can do cheesy. It's that I've been here for just short of 16 years, and no matter how much I try, there is no way I wouldn't forget someone significant if I tried to list all of the people who are important to me here.

Obviously, it's 3.5 years later now. But my attitude on that subject hasn't changed: better to snub everyone equally than to risk snubbing one individual when creating a list of usernames.

I've been on the other side of this, of course. Someone I consider a friend will list the people that mean the most to them on WDC, and I'm not on it. Rationally, I know I'm not everyone's favorite (nor do I seek to be). Monkey brain, though, feels slighted at being left out. I don't want anyone else feeling that way, so, like I said back then:

Everyone that I've interacted with over the years -- occasionally unpleasantly, usually quite the opposite -- has helped to make me what I am today. That includes you, since you're reading this.

One of the major reasons I do these Revisited entries is to see what's changed since the original entry. In this case, it's not much.

Just time.

Fortunately, some cheeses age better than others.

2 Like • Comment • View 2 comments

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