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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.

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September 8, 2019 at 12:09am
September 8, 2019 at 12:09am
PROMPT September 8th

Prompt today is submitted by Elle !

What do you think makes a good leader? Share an example of a good leader from your life (or alternatively, a poor leader who taught you what not to do).

It helps to have rolled a high Charisma score.

Aside from that, well, I think a good leader motivates, encourages, kicks butt when necessary, knows when kicking butt is necessary, reads people, understands a person's strengths and weaknesses, and, probably above all, leads by example.

I worked with a guy for 15 years who mentored me in engineering. He'd answer questions, show me efficient ways to do things, and help keep me focused. We had somewhat different skill sets, at least starting out - I was always the computer nerd, while he was more old-fashioned with a pocket calculator - but gradually we picked up each other's skills.

After those 15 years, he left to start his own company and poached me from our old one; we were both dissatisfied with the way the boss was running things. A bunch of people left all at once. So I started working for him directly, and that's when things started going to shit. He'd emulate our former boss by coming in late, taking long lunches, leaving early, and generally fobbing off most of the work on me. Not a great example. This was especially disappointing to me because, while we were never friends outside of work, I thought we had an understanding. When you know someone for 15 years, you think you actually know them, but things change, I guess.

After a couple of years of this, I left with another of his employees to start our own firm. Karma can be a bitch. At that point, I was still doing all the engineering work (my partner was in another discipline), but at least I was reaping the rewards as well.

My business partner and I never had more than three employees, but I like to think we were better to them than my bosses had been to me. I don't know; I don't have much to compare to. At least I tried to lead by example.

These days, I'm happy being responsible for no one but me and my cats. Not that I don't have other responsibilities, but they're hardly onerous.

I don't know what happened to my former co-worker turned boss, by the way. I hope he ended up successful. I don't hold a grudge; I just couldn't be in that situation any more.

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