Download presentation

Published byMichael Tucker Modified over 4 years ago

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)

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google