Quadratic Functions and Equations Chapter 3 Quadratic Functions and Equations

Complex Numbers 3.3 Perform arithmetic operations on complex numbers Solve quadratic equations having complex solutions

Teaching Example 1 Simplify each expression. Solution

Teaching Example 2 Simplify each expression. Solution

Teaching Example 3 Write each expression in standard form. Solution

Teaching Example 3 (continued) Multiply by Expand. i2 = −1 Simplify.

Teaching Example 4 Simplify each power of i. a. i15 b. i10 Solution

Teaching Example 5 Solve each quadratic equation. Support your results graphically.

Teaching Example 5 (continued) a = 1, b = 4, c = 5

Teaching Example 5 (continued) The graph of does not intersect the x-axis, which indicates that the equation has no real solutions.

Teaching Example 5 (continued) Solution (b) a = 2, b = −3, c = 5

Teaching Example 5 (cont) y1 y2 The graphs of and do not intersect, which indicates that the equation has no real solutions.

Teaching Example 5 (continued) a = −4, b = 0, c = −3

Teaching Example 5 (continued) y2 y1 The graphs of and do not intersect, which indicates that the equation has no real solutions.