Complex Numbers(Under Construction)

(THIS PAGE IS STILL UNDER CONSTRUCTION: MORE TO FOLLOW)

What makes imaginary numbers tough to conceptualize is that they are tough to see.  Negative numbers are easy to see, because we can move backwards beyond zero on a number line. But how can students see imaginary numbers?  Here's one way to present the topic. I would take a poster and roll it into a cylinder and compare it to a number line. See video below.

At times, I think that textbooks place complex numbers too far away from their actual application in solving quadratic equations. Therefore I place them right in my quadratics functions unit as follows.

1. Graphing Quadratics in Vertex Form

2. A Review of Factoring(Binomials, Trinomials, Difference of Two Squares, Perfect Trinomials Squares, and GCF)

3. Solving Quadratic Equations for the purpose of finding zero's of functions, then graphing the quadratic, finding vertex using symmetry)

4. Developing the formula for the vertex of quadratics (x = -b/2a)

5. Solving Quadratics by completing the square{deriving the quadratic formula and eventually using it}

6. Graphing by completing the square and transforming from standard form to vertex form.

7. The discriminant

8. Complex Numbers

    A. Explanation of what they are

    B. Solving Quadratics with complex roots

    C. Relation to transformations

    D. Graphing

    E. Adding and Subtracting

    F. Raising to a power & Developing a pattern

    G. Multiplication, Rationalization, and Absolute Value

9. Application Problems using Quadratics