How Do We Use Imaginary Numbers ?

             Using imaginary numbers is quite simple. First you need to know that " i " is defined as  " √-1 "
                                                         " i=√-1 "
       This is also known as the imaginary unit. We use imaginary numbers, i , to solve the square

 root of negative numbers. For example, we have the square root of -9. The first step to solve 

this is to make -9 positive by making -9 equal to the square root of -1 and positive 9. Knowing 

that the square root of -1 is equal to i, you replace √-1 wit i . Knowing that 9 is a perfect square, 

you can simplify it to 3. When working with imaginary numbers, i come after the real number 

only under the exception that the number is still in square root form. The final answer for the √-9 

is 3i. 


              

         Here's a visual of what i just explained : 

                                     
                                √-9 = √-1 √9

                                      = i√9
                                                            
                                      = 3i 



Now Try It Yourself Using: 


                                √-25

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

         In class, we are always told to flip the inequality symbol when multiplying by a negative number or solving an absolute value inequality. Many of us don't know why we have to flip the inequality symbol. The reason you have to flip the inequality symbol is because when you multiply by a negative number it changes the  way the problem is read.

For instance, take " -5<2 " , which reads -5 is less than 2. This is true because when you look at a number line -5 is less than 2. If I was to multiply both sides by -2, -5 becomes 10 and 2 becomes -4. Writing 10<-4 or 10 is less than -4, is inaccurate. You have to flip the sign to make the inequality true.

          Another example of why you have to flip the inequality sign is if you have 6<12 or 6 is less than 12,and multiply both sides by -3, 6 becomes -18 and 12 becomes -36. Writing -18<-36 or -18 is less than -36 is inaccurate. You have to flip the sign to read -18>-36 or -18 is greater than -36, because on a number line -36 is further from 0 than -18 is, which makes -36 smaller than -18.

Let's check your understanding :

                                                                     Using: 2>-3
                                        Multiply both sides by -3 . What is the new inequality ?