Imaginary numbers are numbers that include a unit of the imaginary number i, which equals the square root of -1. There are two types of numbers, real numbers like integers and rational numbers, and imaginary numbers like 3i. Imaginary numbers are used in calculators by changing the mode to include complex numbers with real and imaginary parts. When working with imaginary numbers, you need to follow rules like not having i in the denominator and using conjugate pairs when dividing. Box diagrams are used to multiply terms with real and imaginary parts, while the quadratic formula can be used to solve quadratic equations that produce imaginary number solutions.

1. Imaginary Numbers By; Samantha Showalter

2. Two types of Numbers There are two types of numbers real numbers and imaginary numbers. Real numbers are numbers such as 1, -2, -1/2, √2, etc.Imaginary numbers are √negatives, √-1= I

3. Example of imaginary number √-9 = 3i √-25 = 5i

4. CalculatorOn your calculator click mode, then go down to where it says real and go over to a+bi and select it. Also to put an I on your calculator you must hit 2nd and the decimal sign.

5. Example problems(3+2i) + (5-6i)= 8-4i (-2-5i) – (3+7i)= -5-12i Those problems you can put in your calculator and they must have parenthesisRule: you cannot have any thing over i^1=I Ex: i^2=-1 because nothing over i^1=I

6. Rule of I This pattern continues on forever.

7. Box problems You will need to use a box problem to work out multiplication of imaginary numbers. For problems that look like this: (3-2i)(5+9i)(4-3i)(6-4i)

8. DivisionRULE: you cannot have an I in the denominator (bottom)/ You have to use the conjugate pair.

9. Example (5-3i)(-3-5i)You would have to multiply both the top and the bottom by the conjugate pair of the denominator.

10. Quadratic formulaYou will plug in the numbers from the problem into the quadratic formula.And solve it like you would when doing a quadratic equation

11. Examples4x^2+7x+35=)A=4B=7C=35Plug into the quadratic formula you get: X=-(7)+or-√(7)^2-4(4)(35)X=-7+or-√-511/8Plug the square root into the calculator.

12. Example cont.You will get X=-7+or- 22.6i/8

13. The end