2. Real Vs. Imaginary Numbers : Real Numbers are numbers that are either irrational or rational such as: -2, 3, 7/8, .25, and pi. Imaginary Numbers are numbers that are complex (numbers you can’t take the square root of). Radical –i : “i” makes the number an imaginary number because the answer is unverifiable.
4. Imaginary Numbers with Addition and Subtraction Addition 7i + 9i Combine like terms (the “i’s go together) So, the answer is: 16i Subtraction 20i – 7i once again combine like terms The answer is: 13i
5. Multiplication and Division Multiplication 3i x 4i (i, just like another number, except to show it’s being multiplied by itself, you square it. What happens when i is squared? i squared is equal to negative one.) So, the answer is: -12 Division -5+9i ÷ 1-i (This is simple. When you write them one above the other, just multiply both top and bottom by the opposite of the denominator. So, the new equation is (-5+9i) x (1+i) all over (1-i) x(1+i). So the answer is: -7+2i
6. Quadratic Formula with Imaginary Numbers Standard Equation: Ax^2 + bx + c = 0 -11x^2 + 7x + -3 Quadratic Formula: so, x = -7 + or – (i) square root of 83, all over -22
