Complex Numbers (Book)

Blog Calendar

◄ February ► 2019
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
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:

Turkey DrumStik

about an hour 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

a day 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

February 22, 2019 at 12:26am

#952718

Loaded For Bear

Feeling less angry today. I think I figured out what it was:

It's freaking February. Yesterday it was cold and there was snow. Today, temperatures got up into the 60s (that's degrees American, of course). Consequently, I had one less thing to be grumpy about, and it made all the difference.

Speaking of cold and other countries:

https://www.theguardian.com/world/2019/feb/13/churchill-canada-polar-bear-capita...

Spend enough time in Churchill, and you will hear the stories.

Of hearing a noise outside, pulling open the drapes and seeing a polar bear looking in through the window.

Okay, that would actually be pretty cool.

Of walking around a corner at night, coming face-to-face with a bear and, implausibly, scaring it off with the strobe light on a cellphone.

I just want to point out that the scary part of that sentence, to me, is not "coming face-to-face with a bear," but the "walking... at night" in freaking northern Canada. I mean, how do you not freeze into a statue three seconds after leaving a warm place, like Lot's wife but with ice instead of salt?

Of being about to, against all better judgment, walk the couple of hundred yards from restaurant to hotel room at night...

Again with the walking at night. What do they serve in that restaurant - anti-freeze?

In fact, the more of that article I read, the more I needed to take a trip to Belize. I can see polar bears at zoos. But in February, I have to travel to get decent weather most of the time.

The bulk of bear viewing takes place on the tundra outside of town, from the safety of bespoke vehicles approximately the size of school buses atop airport fire truck wheels, the immense size of which enables the trucks to traverse treacherous terrain and keep their occupants beyond the reach of even the largest and most curious bear.

In. Theory.

Signs around the town remind residents and visitors alike to exercise caution and report bear sightings on the hotline – 675-BEAR.

Pretty sure that number works in other places, too. But it means something different.

Culvert traps, baited with seal scent, line the perimeter of the community; bears that are caught in them are taken to a holding facility, popularly known as the polar bear jail, where they are held for up to 30 days (without food, to enhance the deterrence factor of the experience)

Because it's such an awesome idea to deliberately make a freaking polar bear hungry.

Ayotte heard Greene’s screams and, clad only in a sweater and his pyjamas, ran toward the scene and brought his shovel down as hard as he could between the bear’s eyes.

Canadians are a lot of things, but easily intimidated ain't one of them.

So anyway, great article, but just reading it made me need a big, roaring fire. Or a tropical beach.

3 Like • Comment • View 5 comments

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