Imaginary numbers? o.O

How do we use imaginary numbers?

Sometimes in Trigonometry, one will have a square root that is negative.

Some thing like this. 

*I know.

* Commonly used in Quadratic Formulas, Imaginary numbers are used to simplify a square root though it is (negative).

*By using an [i] you are able to identify its square or if irrational its simplified form.

*Remember the square root is considered a real number [-36], and [6i] is imaginary

6i

Now one can get something like this, which is irrational.  

         

√-18

√-1 • √18

(√18 = 9•2 = 3•3•2)

i • 3√2

[3i √2]   

 Courtesy of  http://www.regentsprep.org/Regents/math/algtrig/ATO6/SquareRootLes.htm

Flipping inequality symbols :D

"Why do we flip the inequality symbol when multiplying by a negative number or solving absolute value inequalities?"

When one has an absolute value inequality, one must switch the inequality symbol when multiplying by a negative number.

> First always remember that only when multiplying or dividing symbols are switched.
>The reason is because if one does not switch the inequality symbol (depending if its negative) it might not be true.
> Also to address a number line one must make sure a switched is performed.

lets try some and see
5 - 3x [>] 20
try -4
5 - 3(-4) [>] 20
5 + 12 [>] 20
17 [>] 20 

*as you can see not true since the symbol wasn't switched

*Here is how it does work.

5 - 3x [>] 20

 Try -4 ( and switch)

5 - 3(-4) [<] 20

5 +12 [<] 20

17 [<] 20

Courtesy of http://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.101178.html