1. Warm-Up Exercises 1. 52
ANSWER 13 2 2. 15 3
ANSWER 5 15
3x 2 8 23 + = 3.
Solve the equation. 5 – +
ANSWER ( )2 7 + n 4 16 = 4.
ANSWER 5, – 9

2. Warm-Up Exercises
An object falls off a 1000 foot tall building. How long
does it take to hit the ground?
ANSWER
about 7.9 sec

3. Example 1 Solve the equation. = 7x 2 49 – a. b. = 3x 2 5 – 29 SOLUTION
Solve a Quadratic Equation
Solve the equation. =
7x 2 49 – a. b. =
3x 2 5 – 29
SOLUTION
Write original equation. =
7x 2 49 – a.
Divide each side by 7. =
x 2 7 –
Take the square root of each side. = x + – 7
Write in terms of i. = x + – 7 i

4. Example 1 b. = 3x 2 29 – 5 = 3x 2 24 – = x 2 8 – = x + – 8 = x + – 8 i
Solve a Quadratic Equation b. =
3x 2 29 – 5
Write original equation.
Add 5 to each side. =
3x 2 24 –
Divide each side by 3. =
x 2 8 –
Take the square root of each side. = x + – 8
Write in terms of i. = x + – 8 i
Simplify the radical. = x + – 2 i 4

5. Checkpoint Solve the equation. 1. x 2 = – 3 ANSWER 3, i 3 – 2. = x 2 7
Solve a Quadratic Equation
Solve the equation. 1.
x 2 = – 3
ANSWER 3, i 3 – 2. =
x 2 7 –
ANSWER 7, i 7 – 3. =
x 2 20 –
ANSWER 5, 2 5 – i 4. =
x 2 3 2 + –
ANSWER 5, i 5 – 5. =
y 2 4 – 12
ANSWER 2, 2 – i

6. Checkpoint Solve the equation. 6. = 2x 2 7 17 + – ANSWER 3, 2 3 – i
Solve a Quadratic Equation
Solve the equation. 6. =
2x 2 7 17 + –
ANSWER 3, 2 3 – i

7. Write as a complex number in standard form. ( ( 3 + 2i ( + 1 – i (
Example 2
Add Complex Numbers
Write as a complex number in standard form. ( ( 3 + 2i ( + 1 – i (
SOLUTION
Group real and
imaginary terms. 2i 3 ( + i 1 – = 2
Write in standard
form. = 4 + i 7

8. Write as a complex number in standard form. 2i 6 ( – 1
Example 3
Subtract Complex Numbers
Write as a complex number in standard form. 2i 6 ( – 1
SOLUTION
Group real and
imaginary terms. 2i 6 ( = 1 2 i + –
Simplify. = 5 + 0i
Write in standard
form. = 5 8

9. Write the expression as a complex number in standard form.
Checkpoint
Add and Subtract Complex Numbers
Write the expression as a complex number in standard
form. 7. ( 4 – ( 2i ( + 1 + 3i (
ANSWER i 5 + 8. i 3 ( – + 4i 2
ANSWER 3i 5 + 9. 6i 4 ( + 3i 2 –
ANSWER 3i 2 +
10. 4i 2 ( + 7i –
ANSWER 3i 4 –

10. Write the expression as a complex number in standard form.
Checkpoint
Add and Subtract Complex Numbers
Write the expression as a complex number in standard
form.
11. 2i 1 ( – + 5i 4
ANSWER 3i 5 +
12. i 2 ( – 4i 1
ANSWER 3i 3 +

11. Write the expression as a complex number in standard form.
Example 4
Multiply Complex Numbers
Write the expression as a complex number in standard form. a. 1 ( 3i + – 2i b. 3i 6 ( + 3i 4 ( –
SOLUTION
Multiply using distributive property. 1 ( 3i + – 2i =
6i 2 a. 1 ( – 2i 6 = +
Use i 6 2i – =
Write in standard form.

12. Example 4 b. 3i 6 ( + 4 – 24 18i 12i 9i 2 = 24 6i – 9i 2 = 24 6i – 1 (
Multiply Complex Numbers b. 3i 6 ( + 4 – 24
18i
12i
9i 2 =
Multiply using FOIL. 24 6i –
9i 2 =
Simplify. 24 6i – 1 ( 9 =
Use i 6i 33 – =
Write in standard form. 12

13. Write as a complex number in standard form. 2i 3 + 1 –
Example 5
Divide Complex Numbers
Write as a complex number in standard form. 2i 3 + 1 –
SOLUTION 2i 3 + 1 – = •
Multiply the numerator and the denominator by i, the complex conjugate of i.
Multiply using FOIL. 1 2i 3 6i + –
4i 2 = 3 8i + 1 ( – 4 =
Simplify and use i 13

14. Example 5 8i + – 1 5 = 5 1 – 8 i + = Divide Complex Numbers Simplify.
Write in standard form. 14

15. Write the expression as a complex number in standard form.
Checkpoint
Multiply and Divide Complex Numbers
Write the expression as a complex number in standard form.
13. i 2 ( – 3i
ANSWER 6i 3 +
14. ( 2i 1 + i 2 –
ANSWER 3i 4 +
15. i 2 + 1 –
ANSWER 2 1 + 3 i