Aim: How do we use imaginary numbers?

Finding out the meaning of imaginary numbers can be complicated but as long as you know what i represents an imaginary number you'll be alright.
   We define i= √-1 , also called the imaginary unit. We call i the solution to the equation ; i²+1=0 or i²=-1.
       Simplyfying Imaginary Numbers for any Number s,

√-s = i√s

Example : √-9 = √-1√9
= i√9
which equals to 3i

           What is the value of i² ? -1
i³ = i² * i = -1 * i = -i
 and so on .

  

How do we recognize functions?

Recognizing functions is simple, first we have to know the definition of a function.

     A Function is a relation that assigns exactly one output (known as the range) value for each input (know as the domain) value.

 

We recognize functions by making sure the same input value "(x)" is NEVER repeated. We may use

brackets -> { }

Tables, graphs, or mappings.

 

   Some of the characteristics of a function from set A to set B are:

1. Each element of A must be matched with an element B.

2. Some elements of B may not be matched with any elements of A.

3. Two or more elements of A may be matched with the same element of B.

4. An element of A (the domain) cannot be matched with two different elements of B.

 

Example:

  Function: 2x^2+3x+1, we call y a function of x, and use the notation f(x) to represent y.

F(x)= 2x^2+3x+1 .

 

f(x)=x^2-4x ; Find the following...

   A. f(-3)

f(-3)= -3^2 -4(-3)

   9-12=-3

Source: Class notes.