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.

  1. \(2 \boldcdot \sqrt{\text-4}\)
  2. \(3i \boldcdot 2i\)
  3. \(i^4\)
  4. \(4 - 3\sqrt{\text-1}\)
Coordinate plane. Horizontal axis -8 to 8, by 2’s. Vertical axis, -8i to 8i, by 2i’s 

Problem 2

Which expression is equivalent to \((3+9i) - (5-3i)\)?

A:

\(\text-2 - 12i\)

B:

\(\text-2 + 12i\)

C:

\(15 + 27i\)

D:

\(15 - 27i\)

Problem 3

What are \(a\) and \(b\) when you write \(\sqrt{\text-16}\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers?

A:

\(a=0\), \(b=\text-4\)

B:

\(a=0\), \(b=4\)

C:

\(a=\text-4\), \(b=0\)

D:

\(a=4\), \(b=0\)

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.

  1. \(\sqrt{16}\)
  2. \(\text- \sqrt{16}\)
  3. \(\sqrt{\text-16}\)
  4. \(56^{1/2}\)
  5. \(\text- 56^{1/2}\)
  6. \((\text-56)^{1/2}\)
     
Number line, scale -10 to 10, by 2’s.
(From Unit 3, Lesson 10.)

Problem 6

Which expression is equivalent to \(\sqrt{\text-4}\)?

A:

\(\text-2i\)

B:

\(\text-4i\)

C:

\(2i\)

D:

\(4i\)

(From Unit 3, Lesson 11.)