SOLUTION: ((z^3)-(z^2)-4)/(z+i) i need to work it out then state the remainder. It's revision and i cant remember what to do it would be great if i could get some assistance.

Question 288565: ((z^3)-(z^2)-4)/(z+i) i need to work it out then state the remainder.
It's revision and i cant remember what to do it would be great if i could get some assistance.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The division process is shown below in detail.

Original expression is:

First you divide into to get .
Then you multiply by to get .
Then you subtract from to get .
Then you divide into to get .
Then you multiply by to get .
Then you subtract from to get .
Then you divide into to get .
Then you multiply by to get .
Then you subtract from to get .
Then you divide into to get .
Then you multiply by to get .
Then you subtract from to get .
Then you divide into to get .
Then you multiply by to get .
Then you subtract from to get .
Then you bring down the to get .

Since = , you can substitute in this last expression to get:

which becomes:

which becomes:

.

That's your remainder.

Your answer is:

= with a remainder of .

To prove that this is correct, you need to multiply the answer by and then add the remainder back in to see if you can duplicate the original expression.

You do that in the following manner.

* equals:

* plus:
* .

First we multiply * .

That becomes:

.

Then we multiply * .

That becomes:

.

Then we add:

and together to get:

.

Then we combine like terms to get:

.

and canceled out.
and canceled out.
and canceled out.

You are left with:

.

Since = , you can substitute in this expression to get:

= .

You now need to add the remainder of back in.

You get:

plus equals:

.

Combine like results to get:

.

The and the canceled out.

Since this is the same as the original expression you started with, your division is confirmed as being successfully concluded.

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