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 2 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 4 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 1, 2023 at 10:24am

#1042436

Revisited: "Someone's Birthday"

Well, here it is: my first blog post of 2023.

I usually post just after midnight, but obviously I was too drunk to be coherent, so I waited until I was hung over. It may be Amateur Night, but us drinking professionals enjoy it too. It's just that I celebrated at home so I wouldn't have to deal with the amateurs, or get judged by an Uber driver.

I could use this post to look forward to the new year, but that's trite. Or I could make my usual jokes about how you've already failed all of your New Year's Resolutions, but that's even triter; no, I think I'll save that for this week's Comedy newsletter. Alternatively, I could take advantage of the flipping of the calendar to announce a major change in posting format, or a new blog contest that I'll run, but neither of those things are going to happen. Well, the blog contest might happen, but it won't be dependent on some arbitrary odometer change. (I'm toying with the idea of a weekly blogging contest, where I post a prompt and you have six days to take it where it leads you. We'll see.)

But no. If it wasn't Sunday, I'd pull a random article from my still-lengthy queue and rant about it, as per usual. But it is Sunday, and I've been using Sundays to pull the levers on the Wayback Machine, so that's what you get today. Today's blast from the past is from May 10, 2019: "Someone's Birthday"

This is a short one and a response to a 30DBC prompt (I kinda miss that activity, though not enough to jump in and work on it), and, as the title suggests, it celebrates the birthday of Sum1's Home

.

Sum1's Home can be summed up with one word: mushroom. No, wait; that's not it. Toadstool? Well. Some sort of fun guy anyway.

Since I posted this, the author in question changed his username. Oddly, the old links still work. I thought they broke when someone changes their username, but apparently not.

I'm not sure whether this was the first time I made the "fungi" pun in the blog. Probably not; I've been spouting variants of it since high school. It certainly wasn't the last time. I know, I know; it's a morel failing on my part.

After all, Sum1's Home is the curator of "Smile! (Groan?) You Know You Love These!" [13+], which does almost as much to spread laughter as my own comedy does.

And this is how my sense of time sucks: I didn't realize he'd been posting those for so long. It's a regular part of my daily routine to read them.

I don't remember when I first met Sum1's Home. It was probably in the super-secret Moderators forum, which the rest of you can't know about. I know he hasn't been around as long as I have, so really, he's just a kid.

When I wrote that entry, I hadn't met Jim in person. Since then, I've seen him... let's see... four times? Once at dinner with 🌕 HuntersMoon when he was in our area; once on his own turf in Ill-annoy; once when we took a day trip to Newport News for some whiskey; and once when he gave me an excellent bottle of moonshine (and I reciprocated with a bottle of Belizean hot sauce). He gets around because of work. I get around because I like to travel.

So anyway, to be clear, today isn't his birthday; I just landed on that post at random, as per my usual method for finding old blog posts. But, like many people on WDC, I consider Jim a friend and hope we can get together again sometime. After all, I still owe him booze.

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