AF Get-Togethers

[Longhorn]

[REDACTED] [REDACTED]

[Cinjin]

If any of you are ever in Phoenix.....bring sunscreen.

He's just kidding everyone ...

... I think everybody here already knows that one should NEVER go anywhere in Arizona.  

[Minimalist]

Make sure you bring your papers.

[Lemonvariable72]

Hey if any of you guys are ever in the Moncton area hit me up. Kinda hard to miss since its the main land hub for Atlantic Canada.

[Lemonvariable72]

I live in Kent, near Maidstone

If I ever end up in England, which I hope to have a holiday working visa, I'll hit you up. Bewarned I'm especially curious about the Fibonacci sequence and the square root of -1
Edit and pi as I PM'd you before.

[robvalue]

Sounds great

Oh goodie, maths, my favourite! You're welcome to ask anything you like about it in PM or in person.

[Lemonvariable72]

Sounds great

Oh goodie, maths, my favourite! You're welcome to ask anything you like about it in PM or in person.

Okay. What's the deal with √-1?

[robvalue]

Sounds great

Oh goodie, maths, my favourite! You're welcome to ask anything you like about it in PM or in person.

Okay. What's the deal with √-1?

(Edited to remove some wrong info, been a while since I talked about this!)

Lol right! Good question

It's the basis of what we call imaginary numbers. The numbers we usually deal with are called real numbers, this includes all the positive and negative numbers, and all the decimals between each.

We use the letter i to represent the constant of √-1 so that i*i = -1. An imaginary number is then some (real) multiple of i. These numbers don't directly correlate to reality; you can't have 3i of something. Pure mathematics isn't required to have anything to do with reality, only that it is internally consistent. As it happens though, imaginary numbers can help us with reality in an indirect way.

When we add a real number to an imaginary number, we create a complex number (complex as in made up of parts, rather than complicated). So the complex numbers take the form a + bi where a and b are real numbers. This set of complex numbers is now an extension of real numbers.

It has some very useful properties right away, such as giving roots to every polynomial. We often find we have "no solutions" to polynomial equations such as x^2 + 4 = 0. Once we include complex numbers, each polynomial set equal to zero always has a solution.

(A polynomial is a series of terms of the kind ax^n added together, where a is a real number and n is an integer [0, 1, 2, ...] We say the polynomial is of order m, where m is the largest power of x with a non-zero in front of it. All other lesser powers can have a zero or non zero amount.)

Complex numbers have a huge number of applications, the simplest of which is turning a tricky real number problem into the "real part" of a simpler complex number problem, and then extracting the real part again at the end.

That's probably more than you were bargaining for Feel free to ask if anything is unclear, or if you want to know more.

[Alex K]

Also, oddly, quantum waves are described by complex numbers...

[robvalue]

I removed the part about polynomials order n always having n distinct complex roots because I realized that's wrong. Bit rusty They usually do, but sometimes a root can still repeat. They do however always have at least one complex root.