3.2: Imaginary Numbers Objectives: • Define “imaginary” numbers

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Presentation transcript:

3.2: Imaginary Numbers Objectives: • Define “imaginary” numbers • Solve quadratic equations with complex roots.

Concept: Imaginary Unit The reason for the name “imaginary” numbers is that when these numbers were first proposed several hundred years ago, people could not “imagine” such a number. Can you?

Concept: Imaginary Unit cont . . . Imaginary numbers occur when the solution to a quadratic is not in the set of “Real” numbers. (Hence: imaginary) Example: x2 + 2 = 1 – 2 – 2 x2 = –1 √x2 √–1 x = √–1 Note: you can not take the square root of a negative number. (Go ahead, try it on your calculator.) So, now what? x = + i

Concept: Simplifying Negative Radicals

Concept: Simplifying Negative Radicals Your Turn!!! –18 –48 Now, let’s use it when solving equations. We will do everything exactly like we did in the last lesson, but now, we will have a solution, even when the calculator says we don’t. Solve for x: