Lin says, “When you add or multiply two complex numbers, you will always get an answer you can write in form.”

Noah says, “I don’t think so. Here are some exceptions I found:”

1. Check Noah’s arithmetic. Is it correct?
2. Can Noah’s answers be written in the form , where and are real numbers? Explain or show your reasoning.

Explain to someone who missed class how you would write in the form , where and are real numbers.

Which expression is equal to ?

Find the real solution(s) to each equation, or explain why there is no real solution.

Plot each number in the complex plane.

3. -3

Select all the expressions that are equivalent to for all real values of .