Write each power of in the form , where and are real numbers. If or is zero, you do not need to write that part of the number. For example, can be expressed as .
Use any patterns you noticed to rewrite in a similar way. Explain your reasoning.
Use any patterns you noticed to rewrite in a similar way. Explain your reasoning.
11.3
Activity
For each row, your partner and you will each rewrite an expression so it has the form , where and are real numbers. You and your partner should get the same answer. If you disagree, work to reach an agreement.
partner A
partner B
Student Lesson Summary
Suppose we want to write the product in the form , where and are real numbers. For example, we might want to compare our solution with a partner’s, and having answers in the same form makes that easier. Using the distributive property,
Keeping track of the negative signs is especially important since it is easy to mix up the fact that with the fact that .
Next, suppose we want to write the difference as a single complex number in the form . Distributing the negative and combining like terms, we get:
Again, it is important to be precise with negative signs. It is a common mistake to subtract rather than subtracting .
