How Do We Solve Imaginary Number?

We use imaginary numbers to solve problems that need the square root of negative number. 

• We use "i" as an imaginary number which equals to square root of -1.

• i is the solution to the equation i^2+1=0 or i^2=-1.

For example:

            √ -9=√ -1 √ 9
   
             =i√ 9
     
             =3i
                                                                                 

• You always put i after a real number.
• You only put i before a square root or variable.
• If a an answer contains both real number and square root or variable, you  put the i in between. (after the real number and before the square root or variable). 

         


                 
Citation (images):
-http://discoisland.wordpress.com/2010/07/15/true-love-is-less-real-than-imaginary-numbers/
-http://www.google.com/imgres?start=61&num=10&um=1&hl=en&biw=1280&bih=933&tbm=isch&tbnid=Mwd_PZKgZnK56M:&imgrefurl=http://www.mathsisfun.com/numbers/imaginary-
-http://www.coolmath.com/algebra/10-complex-numbers/01-what-are-complex-numbers-01.htm

Why do we sometimes flip the inequality symbols?

When an expression is multiplied or divided by a negative number its preference changes. For example, we have an inequality 8> 4. It means eight is greater than four. Now if we divide or multiply it by -1 it will become -8>-4. However this is incorrect as -4 is greater than -8. Therefore, we need to flip the inequality sign to make the expression mathematically true. So the correct expression is -8<-4, which is mathematically true.

     Citation (images): - http://www.studyzone.org/testprep/math4/d/numberlinel.cfm
                  -http://www.math.com/school/subject2/images/S2U3L4DP2.gif