And so 8 is clearly a member of the real.

So here I'll say that the domain is the set of x's such that x is a member of the real numbers.

So let's see what the real parts are.

This was looking suspicious.

That equals let's see, the real parts.

So pretty much all regular numbers that you ever dealt with before you learned what i was.

I'm saying you can put any real number here, and it's going to map to real numbers.

And our vertical axis is going to be the imaginary part.

You can't add a real number plus an imaginary number.

And then I'll just say for i is less than or equal to n, greater than or equal to 1.

That's just going to be equal to you subtract the real parts. a minus c.

So member of, that's what this little character means.

So we have a complex number here.

double

And in that domain, 2 is sitting there, you have 3 over there, pretty much you could input any real number into this function.

Actually, let me make that clear has a real part and an imaginary part.

Because we're multiplying i times i we get a negative one, but it becomes real again.

I've taken the variable

It's not in the set of reals that's a complex number.

So it would be v1, v2, all the way to vn, where each of these is a member of the real numbers.

But the important thing to realize is essentially you just use the distributive property and realize that you can only add real terms to each other.

I had to get a knee surgery, right?

And just as a little review.

One is a plus bi.

So pi is a real number, e is a real number, square root of 2 is a real number, 3 is a real number, minus 3 is a real number, minus pi is a real number, But 1 plus 2i is not a real number.

So all that's saying is that x1 is a member of the reals, x2 is a member of the reals, all the way up to xn is a member of the reals.

So in this case, if x is real numbers, it's going to map to itself, which is completely legitimate.

And it is a natural number.

So I gave the situation where we have 100 logicians.

The x axis is the real axis.

So you go 1, 2, 3, 4, 5.

So what's the real part?

So only x is equal to 1 would apply to this clause.

So 5 2i.

And that times i, and that's the imaginary part.

So I could really take on any real number.

2 Real Part

Let's say that we weren't dealing with reals.

Ordered 2 tuples where each of the numbers, so you know you could have x1, my 1 looks like a comma, x1 and x2, where each of these are real numbers.

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The greatest common divisor of six and twelve equals six.

You get another complex number.

The real numbers are every number that most people are familiar with, including irrational numbers, including transcendental numbers, including fractions every number is a real number.

This thing here that I just drew the green box around, that's a real number, OK?

Differential equations are something different.