1. Imaginary Numbers By: Austyn Coy

2. Rules/ Things to know with Imaginary Numbers Į = √-1 Į^2 = -1 Your answer cannot have anything over į in it. Standard Form for imaginary numbers is a+ bį. Rational numbers are whole numbers, decimals that end, and perfect squares. Irrational numbers are things like ∏, non perfect squares.

3. Adding Imaginary Numbers To add imaginary numbers you add like terms. (3+2į) + (-5-6į) -2-4į

4. Subtracting Imaginary Numbers To subtract imaginary numbers you subtract the like terms, just like you would adding imaginary numbers. (-7-6į) – (3+2į) -10-8į

5. Multiplying Imaginary Numbers To multiply imaginary numbers you have to distribute to every term in the parenthesis or you could use the box method. The easiest way is to distribute. (3+2į)(6-7į) 32-9į

6. Dividing Imaginary Numbers Rule: You CANNOT have an imaginary number in the denominator. To divide imaginary numbers you have to put everything in parenthesis and multiply by the same equation but the opposite sign. (6 + 2į) (4 + 8į) (4 – 8į) (4+8į) 24 + 48į +8į + 16į^2 8 + 56į 80

7. Quadratic Formula and Imaginary Numbers Standard form – Ax^2 + bx + c X= -b ±√b^2-4ac 2a To use the quadratic formula plug in the a, b, and c into the equation and solve. 5x^2 – 9x + 32 A= 5 B= -9 C= 32 X= 9 ± √-9^2-4(5)(32) 10 X=9± 23.64į 10