Complex Numbers (Book)

Blog Calendar

◄ November ► 2018
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	30
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 7 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!

Nov 14, 2024 at 2:04pm
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

November 29, 2018 at 12:45am

#946502

The Challenge Channel

So, it has come to this: my penultimate entry into "30-Day Blogging Challenge ON HIATUS"

[13+].

We've been asked to come up with potential prompts for future rounds of the contest. Now, keep in mind that for the last 10+ years, I've come up with prompts for "Invalid Item"

approximately once a week, usually at the last minute, but I still have no idea what makes a good prompt - whether for a story or poem, as in the case of the Cramp, or for a blog entry. Still, it's easier to come up with ideas than it is to actually execute them, so let's give this a shot. Grab your donuts.

Write a blog entry from the point of view of your evil (or benevolent, as the case may be) twin. Be sure to have the twin plot your downfall.

Write a letter to your parents from before your birth, warning them about what horrors lurk in their future in the form of you.

Include the following words in your blog entry: syzygy, nihilism, ramifications, turtleneck, and theobromine.

Describe a missed opportunity you encountered, and how things might be different if you hadn't missed it.

Start your blog entry with "So, it has come to this..." and go from there.

Write about an invention that would make your life better... or worse.

Eh, I think I'll stop there. That's six prompts, and I'll have to save some ideas for if I do this challenge again.

One of my favorite things about blogging; that is, one of the reasons I keep doing it in these days of bumper-sticker sound bites, selfies, and superficial life updates, is the opportunity to go into depth about something. I've said before that I'm not one for depth, opting instead for breadth, but some things just can't be expressed with any kind of nuance in 140 characters or fewer. I appreciate one-liners as much as anyone and more than most, but the brief formats of social media just can't do justice to a lot of ideas.

Consequently, when it comes to these blog prompts, I like it when I have to think (but not too hard - that would be work). So if I had to pick my favorite challenge day theme, it'd be "Talk Tuesdays," where I'm sometimes guided to consider things I haven't considered before. But honestly, I've enjoyed most of the prompts, and I've especially liked seeing other points of view on the same topics expressed in other contestants' blogs - and their comments in mine.

In this month-long exercise, I've tried to make the prompts my own, to go beyond what was asked for. But I've also put off writing about some of the things I want to write about. That's okay; I like having a backlog of potential topics, and I can always get to them after tomorrow's final Challenge entry.

I do hope you will stick around for that.

6 Like • Comment • View 6 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.