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