Simplify the following expressions using the imaginary number i: 1. 5√-12 2. √-83. 3√-74. -3√-200 Write the following numbers using the imaginary number i, and then perform the operations necessary and simplify your answer. 3√-9 • 2√-49 √-12 • √-36 i√-36 – i2 Simplify the following expressions using the imaginary number i when needed: 8. i8 9. i75 10. (i2)(i6) Simplify and rationalize the denominators. 11. 4√-3/2 12. -3√-2/27 13. √-4/27 Perform the operation indicated in each problem below: 14. (8 + 6i) + (2 + i) 15. -9+(4-2i)16. (1+i)–(1-i) 17. 3i–(4+15i) Perform the operation indicated in each problem below: 18. (√2 + 3i)(√2 - 3i) 19. (√27 - 3i)(√3 + i) 20. (√2 – i√3) (√2 + i√3) 21. 2i(3i–2) 22. (3 - 6i)2 Determine the sum or difference in geometric terms, and then check it algebraically. Remember that a – b = a + (-b). 23. (8-5i)–(2+3i) 24. (-6 + i) – (-2 -3i) 25. (3 + i) + (-2 + 2i) + (8 - 2i)Solve the following equations using the quadratic formula. 26. X 2 – 4X + 13 = 0 27. X 2 + 49 = 0 28. X 2 + 5X + 8 = 0 29. X2 -3X+4=0
Simplify the following expressions using the imaginary number i: 1. 5√-12 2. √-83. 3√-74. -3√-200 Write the following numbers using the imaginary number i, and then perform the operations necessary and simplify your answer. 3√-9 • 2√-49 √-12 • √-36 i√-36 – i2 Simplify the following expressions using the imaginary number i when needed: 8. i8 9. i75 10. (i2)(i6) Simplify and rationalize the denominators. 11. 4√-3/2 12. -3√-2/27 13. √-4/27 Perform the operation indicated in each problem below: 14. (8 + 6i) + (2 + i) 15. -9+(4-2i)16. (1+i)–(1-i) 17. 3i–(4+15i) Perform the operation indicated in each problem below: 18. (√2 + 3i)(√2 - 3i) 19. (√27 - 3i)(√3 + i) 20. (√2 – i√3) (√2 + i√3) 21. 2i(3i–2) 22. (3 - 6i)2 Determine the sum or difference in geometric terms, and then check it algebraically. Remember that a – b = a + (-b). 23. (8-5i)–(2+3i) 24. (-6 + i) – (-2 -3i) 25. (3 + i) + (-2 + 2i) + (8 - 2i)Solve the following equations using the quadratic formula. 26. X 2 – 4X + 13 = 0 27. X 2 + 49 = 0 28. X 2 + 5X + 8 = 0 29. X2 -3X+4=0
Simplify the following expressions using the imaginary number i: 1. 5√-12 2. √-83. 3√-74. -3√-200 Write the following numbers using the imaginary number i, and then perform the operations necessary and simplify your answer. 3√-9 • 2√-49 √-12 • √-36 i√-36 – i2 Simplify the following expressions using the imaginary number i when needed: 8. i8 9. i75 10. (i2)(i6) Simplify and rationalize the denominators. 11. 4√-3/2 12. -3√-2/27 13. √-4/27 Perform the operation indicated in each problem below: 14. (8 + 6i) + (2 + i) 15. -9+(4-2i)16. (1+i)–(1-i) 17. 3i–(4+15i) Perform the operation indicated in each problem below: 18. (√2 + 3i)(√2 - 3i) 19. (√27 - 3i)(√3 + i) 20. (√2 – i√3) (√2 + i√3) 21. 2i(3i–2) 22. (3 - 6i)2 Determine the sum or difference in geometric terms, and then check it algebraically. Remember that a – b = a + (-b). 23. (8-5i)–(2+3i) 24. (-6 + i) – (-2 -3i) 25. (3 + i) + (-2 + 2i) + (8 - 2i)Solve the following equations using the quadratic formula. 26. X 2 – 4X + 13 = 0 27. X 2 + 49 = 0 28. X 2 + 5X + 8 = 0 29. X2 -3X+4=0
Determine the sum or difference in geometric terms, and then check it algebraically. Remember that a – b = a + (-b).
23. (8-5i)–(2+3i) 24. (-6 + i) – (-2 -3i)
25. (3 + i) + (-2 + 2i) + (8 - 2i) Solve the following equations using the quadratic formula.
26. X 2 – 4X + 13 = 0 27. X 2 + 49 = 0
28. X 2 + 5X + 8 = 0 29. X2 -3X+4=0
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
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