Lesson 14

Select all expressions that are equivalent to \(8+16i\).

\(2(4+8i)\)

\(2i(8-4i)\)

\(4(2i-4)\)

\(4i(4-2i)\)

\(\text-2i(\text-8-4i)\)

Which expression is equivalent to \((\text-4 + 3i)(2-7i)\)?

\(\text-29 - 22i\)

\(\text-29 + 34i\)

\(13 - 22i\)

\(13 + 34i\)

Match the equivalent expressions.

Write each expression in \(a+bi\) form.

1.  \((\text-8 + 3i) - (2 +5i)\)
2.  \(7i(4 - i)\)
3.  \((3i)^3\)
4.  \((3 + 5i)(4 + 3i)\)
5.  \((3i)(\text-2 i)(4i)\)

Here is a method for solving the equation \(\sqrt{5+x}+10=6\). Does the method produce the correct solution to the equation? Explain how you know.

\(\begin{align} \sqrt{5+x}+10 &= 6 \\ \sqrt{5+x} &= \text-4 &\text{ (after subtracting 10 from each side)} \\ 5+x &= 16 &\text{ (after squaring both sides)} \\ x &= 11 \\ \end{align}\)

Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers.

1. \(4(3-i)\)
2. \((4+2i) + (8-2i)\)
3. \((1+3i)(4+i)\)
4. \(i(3+5i)\)
5. \(2i \boldcdot 7i\)