Explain or show how to write \((20 - i)(8 + 4i)\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.

Without writing the left side in the form \(a+bi\), how could you tell that this equation is false?

\((\text-9 + 2i)(10 - 13i) =\text-68 - 97i\)

Andre spilled something on his math notebook, and some parts of the problems he was working on were erased. Here is one of the problems:

\((\underline{\hspace{1cm}} - 2i)(\underline{\hspace{1cm}} + 2i) = \underline{\hspace{1cm}} - 10i\)

1. What could go in the blanks?
2. Could other numbers work, or is this the only possibility? Explain your reasoning.

Find the exact real solution(s) to each of these equations, or explain why there is no real solution.

1. \(x^2=49\)
2. \(x^3=49\)
3. \(x^2=\text-49\)
4. \(x^3=\text-49\)

Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers. Then plot and label each of your answers.

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