A3_Complex Numbers_UA.doc

A3_Complex Numbers_UA.doc - Unit Activity Unit Complex...

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© 2014 EDMENTUM, INC. Unit Activity Unit: Complex Numbers This activity will help you meet these educational goals: Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, use mathematics to model real-world situations, and look for and express regularity in repeated reasoning. Introduction In this unit, you explored complex numbers which are combinations of real and imaginary numbers. In this activity, you will simplify polynomials with complex number factors. __________________________________________________________________________ Directions and Analysis Task 1: Complex Numbers and the Fundamental Theorem of Algebra Look at the graph of the function y = x 2 + 1. You can see that it doesn’t cross the x -axis. This is because when you set y = 0 to find its x -intercept, the equation simplifies to x 2 = -1. As you know, for any real number x , x 2 can never be negative: the square root of a negative number is not a real number. In this task, you will explore the definition and properties of complex numbers so you can find the roots of quadratics such as y = x 2 + 1.
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