Complex Numbers (Book)

Blog Calendar

◄ December ► 2021
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	31
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!

about 2 hours 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

about 4 hours 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.

December 16, 2021 at 12:01am

#1023253

Eight is More Than Enough

As I prepare to face one of my phobias later today, it's only fitting that this story about spiders came up this time.

Why so many of us are casual spider-murderers
It's officially arachnicide season in the Northern Hemisphere. Millions of spiders have appeared in our homes – and they'd better be on their guard. Why do we kill them so casually?

Plus, the new Spider-Man movie hits theaters today. I don't know when I'll get a chance to see it, but I do hope it's soon.

Now, I kind of like spiders. What I mean by that is: when I encounter one outside, I appreciate its elegance and its insectivorous qualities. When I encounter one inside, I try to turn it into an outside spider -- but sometimes, like when I saw a telltale red hourglass marking on one of them, well... things can get ugly.

First I needed to fetch something from the shed – the domain of monstrous spiders the size of baby mice, who lurk in corners with just their furry, gangling legs protruding.

On the other hand, I am not a fan of enormous spiders jumping out at me. That doesn't give me time to do a threat assessment.

Eventually my journey ended on the patio – and here there was a shock. Lying on the paving, legs splayed out wildly, as though he had fallen from a great height – was the pallid corpse of Stripy.

One thing I have never, ever done, though, is give a spider a name. I once had a praying mantis that liked to hang out on my ceiling, and his name was Batman. Mantises (mantes?) share the spiders' penchant for eating annoying bugs without all the extra legs, eyes, and fuzz.

Why do many of us kill spiders so casually, swatting out their lives with our god-like power, almost like it's a reflex?

Because we're bigger (normally) and prefer to remain unbitten?

Spider massacres like these are even more jarring when you consider that spiders and humans are not so different. Though our evolutionary paths diverged at least 530 million years ago, we share many of the same organs and body parts – such as kneecaps – and similar brain chemicals, from dopamine to adrenaline. No one has ever studied spider emotions directly, but it's easy to imagine that they might be more relatable than you would think.

Except I don't like to eat bugs.

They may also have their own unique kind of intelligence, in which they're able to use their webs to help them think.

I've seen articles about this before. The webs act as kind of an external brain. In that, they're not so dissimilar to us, as we use the Web as an external brain.

According to Jeffrey Lockwood, there are a number of reasons we struggle to empathise with spiders – in fact, these unlucky creatures possess a constellation of separate features that chance has combined into a package we find uniquely repulsive.

All those bloody damn eyes, for starters.

Human infants as young as just five months old tend to be more threatened by images of spiders than those of other organisms, suggesting that our aversion to them is partly innate, perhaps having evolved to prevent us from casually picking up ones that are venomous.

I do have a vague memory from early childhood of being freaked out by a spider that was webbing down from the ceiling toward my crib. Though whether that's a memory of a real event or of a nightmare, I'm not certain.

Many of the most chilling stories about spiders have an element of surprise – such as the time a friend donned an old Halloween costume that had been stashed away in the loft for years, and someone said "wow, I love the spider detail on your neck! It's so realistic…". Much screaming ensued, because this was most certainly not part of the look, but a real spider who had silently slunk down from their hat.

This is comedy gold -- if it doesn't happen to me, that is.

Apart from their menacing fangs and scampering legs, spiders face another challenge in the looks department, at least from a human perspective: they don't look like human babies.

To me, this is a point in favor of spiders.

Anyway, a good article to read, and there aren't even that many pictures of spiders to freak people out. The ones that are there are kind of cute. I'm sure most people know intellectually that spiders are our friends, but reason and rationality are poor weapons against the true enemy, which is fear.

I'll have to keep that in mind when I freak out as they drill into my eyeball.

5 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.