# Lesson 13

Multiplying Complex Numbers

### Problem 1

Which expression is equivalent to $$2i(5+3i)$$?

A:

$$\text-6 + 10i$$

B:

$$6 + 10i$$

C:

$$\text-10 + 6i$$

D:

$$10+ 6i$$

### Problem 2

Lin says, “When you add or multiply two complex numbers, you will always get an answer you can write in $$a + bi$$ form.”

Noah says, “I don’t think so. Here are some exceptions I found:”

$$(7 + 2i) + (3 - 2i) = 10$$

$$(2 + 2i)(2 + 2i) = 8i$$

1. Check Noah’s arithmetic. Is it correct?
2. Can Noah’s answers be written in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers? Explain or show your reasoning.

### Problem 3

Explain to someone who missed class how you would write $$(3-5i)(\text-2+4i)$$ in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers.

### Problem 4

Which expression is equal to $$729^{\frac23}$$?

A:

243

B:

486

C:

$$9^2$$

D:

$$27^3$$

### Solution

(From Unit 3, Lesson 4.)

### Problem 5

Find the solution(s) to each equation, or explain why there is no solution.

1. $$2x^2-\frac23= 5\frac13$$
2. $$(x+1)^2=81$$
3. $$3x^2+14=12$$

### Solution

(From Unit 3, Lesson 7.)

### Problem 6

Plot each number in the complex plane.

1. $$5i$$
2. $$2+4i$$
3. -3
4. $$1 - 3i$$
5. $$\text-5 - 2i$$

### Solution

(From Unit 3, Lesson 11.)

### Problem 7

Select all the expressions that are equivalent to $$(3x+2)(x-4)$$ for all real values of $$x$$.

A:

$$3x^2-12$$

B:

$$3x^2-10x-8$$

C:

$$3(x^2 + 2x - 4)$$

D:

$$3(x^2-3x)-(x+8)$$

E:

$$3x(x-3)-2(5x+4)$$

F:

$$3x(x-4)+2(x-4)$$