How do we solve more complex rationals?

How do we solve more complex rationals? 

Complex rationals fall in the same category as complex fractions. So here we'll be doing more practice on it. 

When you get a fraction like ant ordinary, but instead it brings in i. 

You remember i don't you? Imaginary number, it SHOULD ring a bell. But anyways ... 

Where i :

And i goes in a cycle:

So i² = -1, i³ = -i, and i⁴ = 1

For example now, let's say you have a problem including i like this

You'd usually do the numerator and the denominator separate, and then re-write it. 

But here it's different because it's including i and your product won't come out the same. 

So instead you'd multiply the top and the bottom by something to turn the denominator into a whole number. In this case you'd multiply top and bottom by 7 - 4i.

Then you'd cancel out the denominators and multiply the numerators. 

That then simplifies to :

So 43-6i divided by 65 would be your final answer. 

That's about it for the i segment, but here's some more practice on normal complex rationals.

So your problem is this:

Remember you need to have it all simplified before you can do anything. So the numerator would simplify to 3y( y + 7).

Then you'd cross out common factors / multiples. Which would be (y + 7), and you would get your final, simplified answer. 

So that's mostly more practice on complex rationals, fractions, etc. Here's a problem i'll leave if you want to do. (It's not mandatory)

Problem :

Sources:

1. John Schnatterly: johnschnatterly.blogspot.com
2. http://www.mathwarehouse.com/algebra/complex-number/divide/how-to-divide-complex-numbers.php
3. http://www.mathsisfun.com/numbers/imaginary-numbers.html