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

double

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.

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.

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

So that equals a plus b oh sorry.

So let's see what the real parts are.

Choice D.

This was looking suspicious.

Here's the next I want to talk about.

That equals let's see, the real parts.

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

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

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

And in particular, when I divide this, I want to get another complex number.

Practice exercises with fractions

Which of the following complex numbers is represented by the point on the graph below?

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

So we have a complex number here.

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

And just as a little review.

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.

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

And I probably should make a few videos where I classify numbers by reals and complex and irrational and rational and whatever else, and there's actually very formal ways of defining the set of all real numbers, but the simple thing for me is all numbers except complex ones.

I had to get a knee surgery, right?

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

And we are done.

If none of the values is a float, all of them will be treated as integers, and an integer is returned.

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.

So when you add two complex numbers, all you do is you add the real parts to each other and you add the complex parts to each other.

4 Squared Real Part

Practice exercises with fractions

Well this simplifies to I'm going to go back here.

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

And it is a natural number.

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.

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.

And threei we can call an imaginary number.

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