Lesson 11

Introducing the Number $i$

  • Let’s meet \(i\).

Problem 1

Which point represents the complex number \(\text-3 + 2i\)?

Coordinate plane. Horizontal axis, scale -6 to 6, by 2’s. Vertical axis, scale -4i to 4i, by 2i’s. Points plotted, A = -3 comma 2i, B = 3 comma 2i, C = 3 comma -2i, D = -3 comma -2i.
A:

A

B:

B

C:

C

D:

D

Problem 2

Match each expression to an equivalent expression.

A:

\(2i \boldcdot 8\)

B:

\(16i^3\)

C:

\((2i)^4\)

D:

\(2i \boldcdot 8i\)

1:

-16

2:

16

3:

\(\text-16 i\)

4:

\(16i\)

Problem 3

  1. Diego squared a number and got 4. Andre squared a different number and got 4. What were the numbers that Diego and Andre squared?
  2. Jada squared a number and got -4. Elena squared a different number and got -4. What were the numbers that Jada and Elena squared?

Problem 4

Find all solutions to each equation.

  1. \(a^2=1\)
  2. \(b^2=13\)
  3. \(c^2 = \text- 9\)
  4. \(d^2 = \text- 5\)

Problem 5

Find the exact solution(s) to each of these equations, or explain why there is no solution.

  1. \(\sqrt[3]{a+2}=4\)
  2. \(\sqrt[3]{b} +5 = 4\)
  3. \(\sqrt[3]{c-1}-14=\text-4\)
(From Unit 3, Lesson 8.)

Problem 6

Explain how you know that \(\sqrt{\text-1}\) is not a negative number.

(From Unit 3, Lesson 10.)