 # Warm-Up Exercises 1. 52 ANSWER 13 2 2. 15 3 ANSWER 5 15 3x 2 8 23 + =

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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

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

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

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

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

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

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

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

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

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 +

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.

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

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

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

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