1. Warm Up #3 Find the exact value. 2. –√144 1. √49 ANSWER –12 7 ANSWER
2. –√144
1. √49
ANSWER 7
ANSWER
–12 16
3. Use calculator to approximate the value of
to the nearest tenth. 82
ANSWER
2.3

2. Homework Check

5. x x2 1 2 4 3 9 16 5 25 6 36 7 49 8 64 81 10
100 x x2 11
121 12
144 13
169 14
196 15
225 16
256 17
289 18
324 19
361 20
400

6. EXAMPLE 1
Use properties of square roots
Simplify the expression. a. 4 81 = 4 81 =
2 9 b. 7 16 = 7 16 = 4 7

7. GUIDED PRACTICE
GUIDED PRACTICE
for Example 1 9 64
3 8 11 25 5 11 = = 15 4 2 15 7 6 36 49 = =

8. Solve a quadratic equation
EXAMPLE 3
Solve a quadratic equation
Solve 3x2 + 5 = 41.
3x2 + 5 = 41
Write original equation.
3x2 = 36
Subtract 5 from each side.
x2 = 12
Divide each side by 3.
x = + 12
Take square roots of each side.
The solutions are and 12 12 –

9. Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
SOLUTION 15
(z + 3)2 = 7
Write original equation.
(z + 3)2 = 35
Multiply each side by 5.
z + 3 = + 35
Take square roots of each side.
z = –3 + 35
Subtract 3 from each side.
The solutions are – and –3 – 35
The correct answer is C.

12. Solve a quadratic equation
EXAMPLE 1
Solve a quadratic equation
Solve 2x = –37.
2x = –37
Write original equation.
2x2 = –48
Subtract 11 from each side.
x2 = –24
Divide each side by 2.
x = + –24
Take square roots of each side.
x = + i 24
Write in terms of i.
ANSWER
The solutions are i and –i

13. GUIDED PRACTICE
for Example 1
Solve the equation. 2.
x2 + 11= 3. 1.
x2 = –13. 3.
5x = 3 .

14. GUIDED PRACTICE
for Example 2
Write the expression as a complex number in standard form.
7. (9 – i) + (–6 + 7i)
8. (3 + 7i) – (8 – 2i)
9. –4 – (1 + i) – (5 + 9i)
9 – i – 6 + 7i
3 + 7i – 8 + 2i
–4 – 1 – i – 5 – 9i
3 + 6i
-5 + 9i
-10 – 10i

15. Multiply complex numbers
EXAMPLE 4
Multiply complex numbers
Write the expression as a complex number in standard form.
a. 4i(–6 + i)
a. 4i(–6 + i) = –24i + 4i2
Distributive property
= –24i + 4(–1)
Use i2 = –1.
= –24i – 4
Simplify.
= –4 – 24i
Write in standard form.

16. Multiply complex numbers
EXAMPLE 4
Multiply complex numbers
b. (9 – 2i)(–4 + 7i)
= – i + 8i – 14i2
Multiply using FOIL.
= – i – 14(–1)
Simplify and use i2 = – 1 .
= – i + 14
Simplify.
= – i
Write in standard form.

17. Divide complex numbers
EXAMPLE 5
Divide complex numbers
Write the quotient in standard form.
7 + 5i
1  4i
7 + 5i
1 – 4i =
1 + 4i
Multiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i.
7 + 28i + 5i + 20i2
1 + 4i – 4i – 16i2 =
Multiply using FOIL.
7 + 33i + 20(–1)
1 – 16(–1) =
Simplify and use i2 = 1.
– i 17 =
Simplify. 13 17 – = + 33 i
Write in standard form.

18. GUIDED PRACTICE
for Examples 3, 4 and 5
Write the expression as a complex number in standard form.
11.
i(9 – i)
12.
(3 + i)(5 – i)
15 – 3i + 5i – i2
9i – i2
15 + 2i – (-1)
9i – (-1)
15 + 2i + 1
9i + 1
16 + 2i
1 + 9i

19. EXAMPLE 6
Plot complex numbers
Plot the complex numbers in the same complex plane.
a. 3 – 2i
b. –2 + 4i
c. 3i
d. –4 – 3i
SOLUTION
a. To plot 3 – 2i, start at the origin, move 3 units to the right, and then move 2 units down.
b. To plot –2 + 4i, start at the origin, move 2 units to the left, and then move 4 units up.
c. To plot 3i, start at the origin and move 3 units up.
d. To plot –4 – 3i, start at the origin, move 4 units to the left, and then move 3 units down.

20. EXAMPLE 7
Find absolute values of complex numbers
Find the absolute value of (a) –4 + 3i and (b) –3i.
a. –4 + 3i =
(–4)2+32 = 25 5
b. –3i =
02+ (–3)2 = 9 3
0 + (–3i)

21. GUIDED PRACTICE
for Examples 6 and 7
Find the absolute value of:
15.
4 – i
ANSWER 17
16.
–3 – 4i
ANSWER 5
17.
2 + 5i
ANSWER 29
18.
–4i
ANSWER 4

22. Classwork Assignment:
WS 4.5 (13-27 odd) and
WS 4.6 (1-40 multiples of 3)