# Lesson 11

Introducing the Number $i$

### Problem 1

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

A:

A

B:

B

C:

C

D:

D

### Solution

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### Problem 2

Match each expression to an equivalent expression.

### Solution

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### Problem 3

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

### Solution

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### Problem 4

Find **all** solutions to each equation.

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

### Solution

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### Problem 5

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

- \(\sqrt[3]{a+2}=4\)
- \(\sqrt[3]{b} +5 = 4\)
- \(\sqrt[3]{c-1}-14=\text-4\)

### Solution

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(From Unit 3, Lesson 8.)### Problem 6

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

### Solution

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(From Unit 3, Lesson 10.)