# 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

For access, consult one of our IM Certified Partners.

### Problem 2

Match each expression to an equivalent expression.

### Solution

For access, consult one of our IM Certified Partners.

### 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?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

Find all solutions to each equation.

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

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

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

1. $$\sqrt{a+2}=4$$
2. $$\sqrt{b} +5 = 4$$
3. $$\sqrt{c-1}-14=\text-4$$

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 8.)

### Problem 6

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

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 10.)