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 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.

August 21, 2021 at 12:03am

#1015925

Stand-Up Comic

Before I post a link today, I wanted to follow up on yesterday's drink menu. My friend said I should go ahead and post the Lower Drunks recipe, so here it is, along with the modification I made because I couldn't be arsed to make a simple syrup.

The original Lower Drunks:

3/4 oz lemon juice
3/4 oz simple syrup
1 1/2 oz absinthe

Shake with ice. Strain into large martini glass (or rocks glass if necessary). Top with tonic water.

The tonic water is a bit surprising here, but it actually works to cut the overwhelming anise flavor of the absinthe. If you're trying to impress someone, garnish with a curl of lemon peel. Otherwise, who needs a garnish?

Incidentally, a simple syrup is just that: simple. You take equal measures of water and sugar (say, 1 cup each, depending on how much you want to make) and heat it up, stirring until the sugar dissolves. Let it cool. You can store excess (in a closed container) for the next bar session. That's still too much work for me if I'm just trying to drink.

Fortunately, I had some pre-packaged lemon simple syrup, so I just used that instead of syrup + lemon, though I did splash in a bit of lemon juice. That's the modification. It was completely delicious.

Next: we have come up with a recipe (well, mostly she did) for Klingon bloodwine. I will need to replicate her scientific results prior to publishing, though. I must acquire a few ingredients first, and also get off my ass to heat up some sugar water. Stay tuned.

You might have noticed I'm using a different font than usual. There's a reason for that. (Cracked link)

Comic Sans Doesn't Deserve Your Hate

You've heard of using Comic Sans on a resume at your own risk, as it has been deemed inappropriate on so many levels of the "professional" world. Meanwhile, Helvetica is hanging out in the back, laughing in its most pretentious manner. The very thought of selecting this font is often demonized? Even its inventor has admitted that he has only ever used it once -- in a friendly email asking for a refund (and it managed to get his money back). So before you hate, please appreciate that Comic Sans has done some good for someone in this world already.

There used to be a saying circulating around the internet: "There is great need for a sarcasm font." I have pointed out that Comic Sans would fit the bill. No one wants to hear it. It never caught on.

To make the message more fun, he suggested the creation of a new font, one that would mimic the lettering found in comic books rather than a British newspaper.

For the record, British comics use similar lettering to those created in the US. They just spell some shit wrong.

After hitting the general public, bizarrely passionate Comic Sans haters started to make themselves known.

It always struck me as silly that a bunch of people who, mere years before, had no idea what a "font" was, suddenly had Opinions.

He states that he is proud of his work and although the rules of typography have been broken by Connare, one being that the letters don't mirror each other, such as "p" and "q," the manner in which the letters appear have been proven to make it easier for people with reading difficulties. The spacing of the letters allows for a smoother viewing experience, particularly for those with dyslexia.

There you go. A good reason to use comic sans. Or are you going to keep being ableist?

There is a time and a place for Comic Sans, and it usually lies somewhere in between a promotional spring clothing sale banner and a child's bouncy house birthday party.

And, I maintain, for the purposes of conveying sarcasm in a medium that doesn't lend itself to the peculiar vocal tones of sarcasm.

(Note: I don't think WDC uses true Comic Sans, probably because Microsoft has armies of lawyers to rival Disney's. But this is close enough.)

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