Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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:

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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

September 7, 2019 at 12:03am

#965734

Reflection

PROMPT September 7th

Reflect on WDC’s 19th Birthday week! I don’t know any other online community that celebrates like we do

What was your favorite activity to participate in? What is the favorite thing you wrote? What is the favorite thing you read? Did you win anything? (or hope to?

) Tell us!

Yeah... honestly, I didn't do as much as I'd hoped. I've been trying to write at least one contest entry a week all year, but none of the prompts I saw really did it for me, this time. Most of them were about birthdays, and at my age, that's not something I care to think about. Except, of course, when it's my birthday, at which point I want ALL the presents.

So now I'm behind on that. I'm sure I'll be able to catch up, though.

Hey, that's odd. Usually, that sort of thing makes me give something up as hopeless. Maybe I have changed.

Anyway, I was glad to see all the participation. This is a unique venue, as the prompt above alludes, and I like to see it thriving.

Next year is the 20th. Because we're programmed by society to give greater emphasis to numbers that end in 0, I expect that'll be an even bigger deal.

A slightly pedantic aside:

I've seen references to something's nth year. Usually, in context, it goes something like this:

"Jack is 50 years old."

"Amazing! He made it to his fiftieth year!"

While technically correct, if Jack is 50 years old, that means that he also made it to his 51st year.

That sounds odd sometimes, but just think about it: When was your first year? Chances are you don't remember it, but your parents did. They measured your age, then, in months. When you're born, you're 0 years old. A year later, you're 1 year old. In the meantime, you're in your... first year. Consequently, your second year stretches from your first birthday to your second birthday, and so on. When you're 10, you're in your 11th year of life. It's like with centuries: we're in the 21st century, and all the years start with 20.

Put another way, right after you're born, you're not in your 0th year.

You're 29? Then you're either lying, or you're in your 30th year. You can tell someone "I'm 29" or "I'm in my 30th year." The latter will make people think you're 30, because they haven't read this blog entry, so don't do that if you have a youth vanity thing going on.

Point being, as of right now, WDC is in its 20th year, and that's an amazing feat for a relatively small online community.

4 Like • Comment • View 2 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.