Lin says, “When you add or multiply two complex numbers, you will always get an answer you can write in \(a + bi\) form.”

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

\((7 + 2i) + (3 - 2i) = 10\)

\((2 + 2i)(2 + 2i) = 8i\)

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

Explain to someone who missed class how you would write \((3-5i)(\text-2+4i)\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.

Which expression is equal to \(729^{\frac23}\)?

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

1. \(2x^2-\frac23= 5\frac13\)
2. \((x+1)^2=81\)
3. \(3x^2+14=12\)

Plot each number in the complex plane.

1. \(5i\)
2. \(2+4i\)
3. -3
4. \(1 - 3i\)
5. \(\text-5 - 2i\)

Select all the expressions that are equivalent to \((3x+2)(x-4)\) for all real values of \(x\).