So we have two mixed numbers here.

One is a plus bi.

So if I have a plus bi, where a is real and b is real, this is a complex number.

2 Real Part

3 Imaginary Part

And so we could write this.

So we're done.

The negative one times positive eight sixteenth so it's going to be minus, minus eight over sixteen.

So, the first thing I'd like to do here is to just kind of get rid of these parentheses.

So that equals a plus b oh sorry.

So we just have to figure out the real and the imaginary parts.

This is a first degree denominator, and you say, OK.

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

You wouldn't have to have two separate variables here.

5 versus 5.

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

5 Squared Imaginary Part

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

so it would evaluate to 2.

So in in this example, this complex number, our real part is 2.

That's that, and that.

So this part, the integer part, is 3 and the fraction part is 17 40.

4 and 1 8.

That's five.

So all the work we did so far is just to factor out that x to the third minus 8, but now we can actually do some partial fraction expansion, or partial fraction decomposition.

Nothing fancy here. z sub one minus z sub two.

And that's the new real part.

The x axis is the real axis.

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

So 5 2i.

But experimental science had been tied up with all those things.

This part right here is the real part.

And so on our original problem up here, we now know that b is equal to 3, c was equal to 4, and a is equal to 7.

But your numerator is going to be your numerator of the fraction part before.

little bit of both.

To the 10th power.

And we are done.

We have a 2 and we have a positive 15

So let's say we had 1 and 5 8 plus 2 and 4 8.

So then, what are our real parts?

So it's a and c.

You could say, well, this is just going to be equal to take the real part squared.

Let's see if we can learn a thing or two about partial fraction expansion, or sometimes it's called partial fraction decomposition.

There is 1 last key element of a computer program.