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High School — Mathematics
Number, Number Sense and Operations

Overview

Core Resources

    Number, Number Sense and Operations

    Strategies

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      Online Resources

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      Strategies: Advanced Work

      The following activities are suggestions for working with students who are ready for advanced work. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Imaginary Numbers

      After exploring real numbers, students can study the imaginary numbers. Imaginary numbers are the square roots of negative numbers. Together with the real numbers they form the set of complex numbers.


      Problem

      What are all solutions to the equation over the set of imaginary numbers?

      Method

      This question asks us to find all solutions to the equation instead of just the real solutions. Therefore, we need to consider those answers that are the square roots of negative numbers. To solve the equation, we solve for .

      Then we take the square root of both sides.

      Usually is rewritten as . Therefore, our solution is .

      Answer

      Extension

      When students are familiar with complex numbers, they are ready to understand how to visualize these numbers on the complex plane. Students should be able to graph complex numbers on this plane.

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