# Lesson 14

More Arithmetic with Complex Numbers

- Let’s practice adding, subtracting, and multiplying complex numbers.

### Problem 1

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

\(2(4+8i)\)

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

\(4(2i-4)\)

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

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

### Problem 2

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

\(\text-29 - 22i\)

\(\text-29 + 34i\)

\(13 - 22i\)

\(13 + 34i\)

### Problem 3

Match the equivalent expressions.

### Problem 4

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

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

### Problem 5

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.

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

### Problem 6

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

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