Complex solutions are not always simple to find. In the fourth instructional activity of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first instructional activity. In solving quadratic equations by completing the square, a helpful hint on creating equivalent equations makes the process easier to handle. The last portion of the instructional activity reminds the class of the geometric interpretation of i and has them determine the geometric meaning of powers of the imaginary unit.

Concepts

complex numbers, complex plane, complex roots, quadratic equations, imaginary numbers, rotations

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Additional Tags

math

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Instructional Ideas

• Review solving quadratics with real solutions prior to working with quadratics with complex solutions
• Have individuals keep a journal for the unit where they can write their responses to questions posed during the lesson

Classroom Considerations

• The class should be familiar with the geometric representation of i

Pros

• The lesson uses a graphical display to help with completing the square
• The answer sheet shows the work students should show to arrive at the solution

Cons

• None

Common Core

HSN-CN.A.3 MP3