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For homework, Crystal must simplify the expression . She gets the answer , but when she checks, she learns that the correct answer is .

  1. Show Crystal the steps she could take to get .

  2. What steps do you think Crystal took to get as a result?

    What is ?

  3. What does she need to consider to avoid making this mistake in the future?

    She needs to convert to imaginary form before completing operations.

  4. Crystal’s example means that is not always true for real numbers and . What restriction needs to be placed on the numbers and ?

    They must be non-negative real numbers.