# Lesson 14

More Arithmetic with Complex Numbers

### Problem 1

Select all expressions that are equivalent to $$8+16i$$.

A:

$$2(4+8i)$$

B:

$$2i(8-4i)$$

C:

$$4(2i-4)$$

D:

$$4i(4-2i)$$

E:

$$\text-2i(\text-8-4i)$$

### Solution

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### Problem 2

Which expression is equivalent to $$(\text-4 + 3i)(2-7i)$$?

A:

$$\text-29 - 22i$$

B:

$$\text-29 + 34i$$

C:

$$13 - 22i$$

D:

$$13 + 34i$$

### Solution

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### Problem 3

Match the equivalent expressions.

### Solution

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### Problem 4

Write each expression in $$a+bi$$ form.

1.  $$(\text-8 + 3i) - (2 +5i)$$
2.  $$7i(4 - i)$$
3.  $$(3i)^3$$
4.  $$(3 + 5i)(4 + 3i)$$
5.  $$(3i)(\text-2 i)(4i)$$

### Solution

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### Problem 5

Here is a method for solving the equation $$\sqrt{5+x}+10=6$$. Does the method produce the correct solution to the equation? Explain how you know.

\begin{align} \sqrt{5+x}+10 &= 6 \\ \sqrt{5+x} &= \text-4 &\text{ (after subtracting 10 from each side)} \\ 5+x &= 16 &\text{ (after squaring both sides)} \\ x &= 11 \\ \end{align}

### Solution

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(From Unit 3, Lesson 7.)

### Problem 6

Write each expression in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers.

1. $$4(3-i)$$
2. $$(4+2i) + (8-2i)$$
3. $$(1+3i)(4+i)$$
4. $$i(3+5i)$$
5. $$2i \boldcdot 7i$$

### Solution

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(From Unit 3, Lesson 13.)