Complex Numbers (Book)

Blog Calendar

◄ February ►
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 16 hours ago
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

about 22 hours ago
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

a day ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

a day ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

Dec 26, 2024 at 10:00am
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

February 17, 2024 at 9:04am

#1064327

Inside Voice

Bit out of the ordinary for me today—a link sent by a friend:

Some People of Color Don't Like the Outdoors and That's Okay

As I, too, shun the not-so-great outdoors, I found great wisdom in these words.

The outdoor industry has spent hundreds of millions in marketing dollars to convince you that everyone belongs outside.

To be fair, lots of industries spend lots of money trying to convince us that everyone needs their products.

That simply isn’t true. Some People of Color aren’t outside for very valid reasons.

As far as I'm concerned, every reason is a valid reason, but I can only imagine how much worse it must be when you have to be concerned that racist rednecks love to be outdoors. With guns.

Some don’t like the outdoors and that’s okay.

"I don't like it" is a valid reason. So is "I don't want to."

They don’t need you to convert them. Unless, maybe, you’ve found the perfect beginner-friendly hike that ends in a waterfall and free universal healthcare.

Okay, that bit made me laugh.

But failing that, here are eight reasons why you should leave your friends and family alone.

Oddly, like Cracked (which this isn't from), it's a countdown list. I won't be covering everything.

Some of us occupy entirely different realities from our parents. For us, sleeping on the ground is an adventure. For them, sleeping on the ground is elective poverty and strange (or a bad memory). Why would they pay to do that?

I've gone on about this sort of thing before. You live in a nice house, and you want to experience two weeks of homelessness? With bears and snakes? Okay, you do you, but count me out.

Some of your friends aren’t interested in hiking or climbing because they can’t afford to get hurt and miss work. They also can’t afford medical care.

Laaaaand... of the... freeeeeee!

And yes, you can get hurt at home, too. But I'm pretty sure the chances of that go up in areas of uncertain footing, wild animals, and stinging insects.

4. They don’t want to get their hair wet

This section turned out to be important for me to read, because I was mostly unaware of this aspect of culture.

3. They don’t have the money

We like to pretend that being outside doesn’t cost a thing. And it’s weird. Stop that.

While poverty looks different for different people, this point is something to remember when considering a trip to the not-inside. Proper gear (which I'm sure would help reduce the chance of injury, as above) can get expensive. Even those not experiencing poverty might have better (to them) things to spend money on.

Why do we pretend that the outdoors costs nothing—that you are required to bring nothing but yourself? Then in the next breath we shame hikers who don’t bring reusable water bottles, moisture wicking technical clothing, wool base layers, wind and water resistant shells, puffers, GPS, a trail map subscription with downloaded maps, a paper map and compass, etc.

I read an article about someone who died on Mount Washington in New Hampshire last month. The article described him as an "experienced hiker." Now, I certainly don't claim to be an expert on mountaineering, though, yes, I've hiked mountains, and experienced firsthand how quickly the weather can turn on you there. And I've read that Mount Washington is the worst of the bunch, being well-known for having logged the highest recorded non-cyclonic wind speed of any point on Earth. So my first thought was "Funny; I thought 'experienced hikers' don't mess with Mount Washington in fucking January."

It’s winter now and social media is full of photos and videos of happy people skiing, snowshoeing, tubing and snowboarding.

One of those things is not like the others...

Anyway, while a lot of the cultural reasoning doesn't apply to me, and to be fair, I was privileged enough to spend a lot of time outdoors as a child and young adult before deciding I just didn't like it, I appreciate the article's perspective. And to be clear, it's not "being outside" that I dislike; it's being farther than a short walk from civilization.

Now watch, some marketing guru is going to try to take all the stuff in that article into account the next time they need to market a line of rugged-yet-fashionable outdoor wear that'll be lucky to last for a year.

3 Like • Comment • View 5 comments

© Copyright 2024 Waltz Invictus (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz Invictus has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.