3.5 Complex Numbers Application

Name: ________________________ Class: ___________________ Date: __________ 3.5-Complex Numbers Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the real and imaginary part of the complex number 8 – 3i. a. Real part = –3, Imaginary part = 8. b. Real part = 8, Imaginary part = –3. c. Real part = 3i, Imaginary part = 8. d. Real part = 8, Imaginary part = –3i. ____ 2. Find the real and imaginary parts of the complex number. 8 a. b. c. ____ Real part 8, imaginary part 8 Real part 0, imaginary part 8 Real part 8, imaginary part 0 3. Find the real and imaginary part of the complex number a. b. c. d. 3 10 . 3 , Imaginary part = 10 Real part = 10 , Imaginary part = 3 Real part = 3, Imaginary part = –10 Real part = 3 , Imaginary part = 10 Real part = ____ 4. Evaluate the expression (9 + 14i) + (7 – 11i) and write the result in the form a + bi. a. 16 + 3i b. 9 + 14i c. 3 + 16i d. 16 – 3i ____ 5. Evaluate the expression 10(–2 + 14i) and write the result in the form a + bi. a. 20 – 140i b. –20 + 140i c. –140 + 20i d. –140 – 20i ____ 6. Evaluate the expression (4 + 9i)(11 – 10i) and write the result in the form a + bi. a. 44 + 99i b. –59 – 134i c. 59 + 134i d. 134 + 59i ____ 7. Evaluate the expression i 17 and write the result in the form a + bi. a. 1 b. –1 c. –( i ) d. i 1 ID: A Name: ________________________ ID: A ____ 8. Evaluate the expression i 64 and write the result in the form a + bi. a. –i b. i c. –( 1 ) d. 1 ____ 9. Evaluate the expression a. b. c. d. 8 + 9i 9 + 8i 9 – 8i –8 – 9i ____ 10. Evaluate the expression a. b. c. d. 4  10i and write the result in the form a + bi. 2i 10 – 4i –5 + 2i 2 – 5i 5 – 2i ____ 11. Evaluate the expression a. b. c. d. 145 and write the result in the form a + bi. 9  8i 35 40  and write the result in the form a + bi. 2i 2i 15 – 2i 2 + 15i –15 – 2i 2 – 15i ____ 12. Evaluate the expression a. 2i b. –2 c. –2i d. 2 4 and write the result in the form a + bi. ____ 13. Evaluate the expression a. 18 b. –18i c. –18 d. 18i 4 Ê ____ 14. Evaluate the expression ÁÁÁ 4  Ë a. 52 + 12i b. 12 – 52i c. –20 + 12i d. 32 + 32i 81 and write the result in the form a + bi. ˆÊ 16 ˜˜˜ ÁÁÁ 8  ¯Ë ˆ 25 ˜˜˜ and write the result in the form a + bi. ¯ 2 Name: ________________________ ____ 15. Evaluate the expression a. b. c. d. ID: A 1,225 5 49 and write the result in the form a + bi. i 5  5 5i i 5 ____ 16. Find all solutions of the equation x 2 + 49 = 0 and express them in the form a + bi. a. x = 7i b. x = 7i, x = –7i c. x = 7i, x = –7 d. x = 7, x = –7 ____ 17. Find all solutions of the equation x 2 – 8 x + 25 = 0 and express them in the form a + bi. a. x = 4, x = –4 b. x = 4 + 3i, x = 4 – 3i c. x = 3 + 5i, x = 3 – 5i d. No solutions ____ 18. Find all solutions of the equation 2 x 2 – 12 x + 20 = 0 and express them in the form a + bi. a. No solutions b. x = 1 + 4i, x = 1 – 4i c. x = 3, x = –3 d. x = 3 + 1i, x = 3 – 1i ____ 19. Find all solutions of the equation z  8  a. b. c. d. 20  0 and express them in the form a + bi. z z = 2 + 5i, z = 2 – 5i No solutions z = –4 + 2i, z = –4 – 2i z = 4, z = –4 Numeric Response 1. Evaluate the expression and write the result in the form a  bi. 5 75 1 3 Short Answer 1. Perform the addition and write the result in the form a  bi. (2  4i)  (4  3i) 3 Name: ________________________ ID: A 2. Perform the subtraction and write the result in the form a  bi. ÊÁ ˆ Ê ˆ ÁÁ 4  3 i ˜˜˜  ÁÁÁ 3  9 i ˜˜˜ ÁÁ ˜ Á 2 ˜¯ ÁË 2 ˜˜¯ Ë 3. Perform the subtraction and write the result in the form a  bi. (0.3  1.5i)  (1.2  3.6i) 4. Evaluate the expression and write the result in the form a  bi. ÊÁ 1 ˆ˜ 8i ÁÁÁ  i ˜˜˜ ÁË 8 ˜¯ 5. Evaluate the expression and write the result in the form a  bi. (7  i)(3  3i) 6. Evaluate the expression and write the result in the form a  bi. ÊÁ 2 ˆÊ ˆ ÁÁ  24i ˜˜˜ ÁÁÁ 1  12i ˜˜˜ ÁÁ 3 ˜˜ ÁÁ 6 ˜˜ Ë ¯Ë ¯ 7. Evaluate the expression and write the result in the form a  bi. i 1.003 8. Evaluate the expression and write the result in the form a  bi. 3i 2  3i 9. Evaluate the expression and write the result in the form a  bi in simplified form. 26  39i 2  3i 10. Evaluate the expression and write the result in the form a  bi. (5  4i) 1 11. Evaluate the expression and write the result in the form a  bi. (1  4i)(3  i) 2i 4 Name: ________________________ ID: A 12. Evaluate the expression and write the result in the form a  bi. ÊÁ ÁÁ Ë 3 ˆÊ 4 ˜˜˜ ÁÁÁ ¯Ë 6 ˆ 8 ˜˜˜ ¯ 13. Find all solutions of the equation and express them in the form a  bi. 25x 2  16  0 14. Find all solutions of the equation and express them in the form a  bi. 2x 2  4  2x 15. Find all solutions of the equation and express them in the form a  bi. z8 96 0 z 16. Find all solutions of the equation and express them in the form a  bi. 1 2 x  5x  25  0 2 5