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:

Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day 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

Nov 14, 2024 at 12:10pm
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

January 18, 2019 at 12:31am

#949906

Food for Thought

How much do you know about food waste in your country? Spend some time researching this issue and share a fact you learned. How conscious of your access to food are you and in what ways can you be more responsible for reducing your own food waste?

I waste food.

One of the few disadvantages of effectively living alone (my housemate and I don't normally share food) is that packaging at stores is designed for families, not individuals. So I'll buy, for example, a pint of strawberries, eat half of them, and then by the time I go to eat the other half, they're a biology experiment.

Sometimes it's only a couple of strawberries that are fuzzy, but honestly, once I see that mold, I lose all appetite for strawberries. Consider the environment lucky if I bother to compost the strawberry mold and chuck the container into recycling.

Avocados are even more dicey (see what I did there?) This is the life cycle of an avocado:

1) Purchase firm, green avocado.
2) Let it sit on the counter while it ripens.
3) Toss mushy, black avocado into trash.

But that's just me. To look at food waste in general, I went here.

The article's two and a half years old now, but I doubt much has changed in that time.

Hey, we're #1 in something besides incarceration!

Now, understand, I'm wary of anything purporting to know the cause of something without scientific evidence. But I am aware that, rather than donate food scraps to shelters or feed them to the homeless, supermarkets hit them with bleach before throwing them away. I understand why they do that, but on a visceral level it just seems wrong.

We live in a time of abundance. This is, in general, a good thing. Those of us with money want for no essentials.

My parents were shaped by a different time. They were both children of the Great Depression, and it showed in their attitude toward waste. There was something about that time that engendered something akin to PTSD - a deep-set attitude that there might not be supplies tomorrow. My father designed our house to use passive solar in a bid to save energy before anyone had even heard of passive solar. We dumped food scraps into the garden to enrich the soil for food we grew ourselves. We recycled before recycling was a trend. And my parents never, ever let food go to waste.

And like any rotten kid, I rebelled against their attitude of scarcity. Now that I'm their age, though, I've begun to see their point. Also like any rotten kid.

Now, our culture is all about disposability. The idea of saving - be it money, food, or whatever - is alien to us. Hell, people mock hoarders, and there's a pervasive attitude that there's no point to saving money against future times of need. It's not just food we throw away, it's everything - including things that, when we got them, were supposed to improve our lives or help us be comfortable and happy.

The Great Depression began 90 years ago this fall, so there aren't so many alive anymore that remember it. And thus, we're doomed to repeat the mistakes we didn't learn from history.

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