Math Worksheets

Archive for January, 2009

Question: I need help with Algebra, Imaginary expressions?

Alright. So I’ve missed 3 days of school so far, and I’m a little worried about catching up in math… My teacher emailed me the notes, but she usually does the examples for them up on the board. So I have the examples, but no answer for them or how to solve. What we’re doing right now is “simplifying complex number expressions”

Right now, we’re talking about imaginary numbers, I guess… The square root of a negative number…

So, one example is

-24 (With one of those little check mark line things above it.. I don’t know what it’s called)
And I’m not sure how to do it. I know from a different example that -3=i. And the answer is 3.
Another one was -4=i. And 2i is the answer.

So, how would I do the ones I’m having trouble with? I have a whole worksheet to do on this and I’m stuck!
Can someone please explain how to solve:

1) -24
2) -15
3) -64

Thanks you!

Answer: Here is the trick, a negative= i
so -1=i
so square root(the check mark thing) -24
so you have to pull out the i
so it would be i check mark 24
and the square root of 24 is 4 times 6 so 2×2x2×3 so the answer is:
2i check mark 6

check mark -15
again, pull out the i (which is the negative one, got it?)
i check mark 15
since 15 can’t reduce anymore for a square root, that is your answer

-64
this one is easy
pull out the i
so its i check mark 64
and what is the square root of 64?
It’s 8
so the answer is 8i

I.M. me if you are having trouble

Hope I helped!

Graphing an Inequality on a Number Line

So, we have zero on top of two and underneath. Then treating each column separately, we subtract 253 by whatever number B is underneath 2 which in this case is zero. That gives 253 again. Now you may think we have not gotten anywhere but in Long Division, we have progressed. We are done with the first column so now it’s time to move to the second column.

Now, for any column, you want to take care of the number in that column and any numbers to the left of it. In this case, the number in the second column is 5 but 2 still remains in the first column so you have 25 to work with in the second column. So, how many times can 5 divide into 25? The answer is 5, so A for the second column is 5 and you write 5 on top. (where the blue question-mark is). At the bottom, B is 5 times 5 which is 25 so you write 25 at the bottom.

now treating each column separately, we subtract 25 from 253. The first column is zero and so is the second column. That leaves the third column as three. Now we want to divide 5 into 3. However, since 3 is smaller than 5, 5 can divide into 3 zero times. So, we again write zero on top of the roof in the third column and at the bottom write B = 5 x 0 = 0. That means the remainder is 3 or we can keep the Long Division going.

So, for this Long Division, 253 divided by 5 is 50 with the remainder of 3.