How to solve an imaginary number?

*Note: sorry for the late post guys my power went out multiple times throughout the week since Sunday and i wasn't able to post it.

How to solve imaginary Numbers?

What are imaginary Numbers? 

A imaginary number is a number whose square is less than or equal to zero.  Imaginary numbers are shown through the symbol of   .

The reason why a imaginary number is used is to find the square root of a negative number or multiply a number by itself in order to get a negative product.

For example:

*=sqrt(-1) OR 


What can be do with it?
by taking the square root of both sides we can get:
= sqrt(-1)
meaning that  is the square root of -1

This is great because by thinking in terms of  or that  exists it is easier to solve problems with a negative square root.
LETS SOLVE A PROBLEM:
sqrt(25*-1)= sqrt(25)*sqrt(-1)= 5*sqrt(-1)= 5

In other words: √(-x) = i√x

The Interesting Property.

 has an interesting property which consists of it going through four different values each time you multiply. Which are: 

*=-1

*-1= -

-*= 1

*1=

 OR CAN BE SEEN IN EXPONENTS LIKE SHOWN BELOW:

i = √-1

i2 = -1

i3 = -√-1

i4 = 1

i5 = √-1

........etc

TRY IT YOURSELF:

Solve the following questions:

1.What is the square root of -49?

2. 

What is i⁶

Websites used:

http://www.mathsisfun.com/numbers/imaginary-numbers.html

http://en.wikipedia.org/wiki/Imaginary_number

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

Question: Why do we flip the inequality symbol when multiplying and dividing by a negative number or solving absolute value inequalities?

Answer:

     The reason why we flip the inequality symbol when multiplying and dividing by a negative number is to keep a balance between both sides of the inequality symbol.  This action can be seen In 50>5 or 50 is greater than 5 where after (-1) is multiplied or divided to the problem it becomes -50<-5.  The reason the signs are switched is to make the problem true(accurate) instead of false(inaccurate).  In other words if a number was negative before it becomes positive and if a number was positive before it becomes negative, this occurs to both numbers on both sides of the inequality.When this happens the number that was less than before is now greater than and the number that was to the right(greater than) ends up to the left of ( or less than) the other number.  This is why we have to flip  the inequality sign whenever we multiply or divide by a negative number.

NOW TRY IT YOURSELF!!!   

For which problem do we have to switch the inequality sign?

A.)20x>2
B.)10x>8
C.)-5x>-15
D.)35x>7