Lesson 12
Arithmetic with Complex Numbers
 Let’s work with complex numbers.
Problem 1
Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers. You may plot the numbers in the complex plane as a guide.
 \(2 \boldcdot \sqrt{\text4}\)
 \(3i \boldcdot 2i\)
 \(i^4\)
 \(4  3\sqrt{\text1}\)
Problem 2
Which expression is equivalent to \((3+9i)  (53i)\)?
\(\text2  12i\)
\(\text2 + 12i\)
\(15 + 27i\)
\(15  27i\)
Problem 3
What are \(a\) and \(b\) when you write \(\sqrt{\text16}\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers?
\(a=0\), \(b=\text4\)
\(a=0\), \(b=4\)
\(a=\text4\), \(b=0\)
\(a=4\), \(b=0\)
Problem 4
Fill in the boxes to make a true statement:
\(\displaystyle (\boxed{\phantom{30}}3i)  (15+\boxed{\phantom{30}}i) = 7  12i\)
Problem 5
Plot each number on the real number line, or explain why the number is not on the real number line.
 \(\sqrt{16}\)
 \(\text \sqrt{16}\)
 \(\sqrt{\text16}\)
 \(56^{1/2}\)
 \(\text 56^{1/2}\)

\((\text56)^{1/2}\)
Problem 6
Which expression is equivalent to \(\sqrt{\text4}\)?
\(\text2i\)
\(\text4i\)
\(2i\)
\(4i\)