# Lesson 12

Arithmetic with Complex Numbers

### Problem 1

Write each expression in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers. You may plot the numbers in the complex plane as a guide.

1. $$2 \boldcdot \sqrt{\text-4}$$
2. $$3i \boldcdot 2i$$
3. $$i^4$$
4. $$4 - 3\sqrt{\text-1}$$

### Problem 2

Which expression is equivalent to $$(3+9i) - (5-3i)$$?

A:

$$\text-2 - 12i$$

B:

$$\text-2 + 12i$$

C:

$$15 + 27i$$

D:

$$15 - 27i$$

### Problem 3

What are $$a$$ and $$b$$ when you write $$\sqrt{\text-16}$$ in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers?

A:

$$a=0$$, $$b=\text-4$$

B:

$$a=0$$, $$b=4$$

C:

$$a=\text-4$$$$b=0$$

D:

$$a=4$$, $$b=0$$

### Problem 4

Fill in the boxes to make a true statement:
$$\displaystyle (\boxed{\phantom{30}}-3i) - (15+\boxed{\phantom{30}}i) = 7 - 12i$$

### Problem 5

Plot each number on the real number line, or explain why the number is not on the real number line.

1. $$\sqrt{16}$$
2. $$\text- \sqrt{16}$$
3. $$\sqrt{\text-16}$$
4. $$56^{1/2}$$
5. $$\text- 56^{1/2}$$
6. $$(\text-56)^{1/2}$$

### Solution

(From Unit 3, Lesson 10.)

### Problem 6

Which expression is equivalent to $$\sqrt{\text-4}$$?

A:

$$\text-2i$$

B:

$$\text-4i$$

C:

$$2i$$

D:

$$4i$$