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Page 300

Page 300. Complex Solutions. Complex Numbers. Complex Numbers are numbers that are associated with a second real number with an ordered pair a + b i Conjugate is the complex number’s opposite sign Example: 2 + 3 i ‘s conjugate is 2 – 3 i

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Page 300

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  1. Page 300 4.5 - Complex Numbers

  2. 4.5 - Complex Numbers

  3. Complex Solutions 4.5 - Complex Numbers

  4. Complex Numbers Complex Numbersare numbers that are associated with a second real number with an ordered pair a + b i Conjugate is the complex number’s opposite sign Example: 2 + 3i ‘s conjugate is 2 – 3i Remember: NO IMAGINARY NUMBERSin the denominator SIMPLIFY RADICALS FIRST then OPERATE Imaginary Number Real Number 4.5 - Complex Numbers

  5. Example 1 Find the values of x and y that make the equation 4x + 10i= 2 – (4y)itrue. Real parts 4x + 10i = 2 – (4y)i Imaginary parts 4.5 - Complex Numbers

  6. Example 2 Find the values of x and y that make the equation 2x – 6i= –8 + (20y)itrue. 4.5 - Complex Numbers

  7. Your Turn Find the values of x and y that make the equation true. 4.5 - Complex Numbers

  8. Imaginary Numbers Rules with Imaginaries: i1 = i i2 = –1 Answers CAN have an i but CAN NOT have two i’s Two i’s make –1 4.5 - Complex Numbers

  9. Example 3 Solve the equation, 5x2 + 90 = 0 4.5 - Complex Numbers

  10. Your Turn Solve the equation, 9x2 + 25 = 0 4.5 - Complex Numbers

  11. Example 4 Solve the equation, 3x2 – 2x + 5 = 0 4.5 - Complex Numbers

  12. Your Turn Solve the equation, 2x2 + x + 3 = 0 4.5 - Complex Numbers

  13. Cube Roots 4.5 - Complex Numbers

  14. Sum and Difference of Cube Roots • Take the GCF Out • Put the equation into perfect cubes • Put the bases of the cubes into parentheses • Refer to the bases in the parentheses and follow the format of S1OMAS2 S1 – Square the first base O – Take Opposite of the original problem’s sign M – Multiply the first and second base (leave the signs alone) A – Put addition sign S2 – Square the second base 4.5 - Complex Numbers

  15. Example 5 Solve the equation, x3 + 27 = 0 4.5 - Complex Numbers

  16. Example 6 Solve the equation, x3 – 27 = 0 4.5 - Complex Numbers

  17. Example 7 Solve the equation, x3 – 1 = 0 4.5 - Complex Numbers

  18. Your Turn Solve the equation, x3 + 64 = 0 4.5 - Complex Numbers

  19. Review Rationalize What is the problem with the bottom? We try to get rid of the radicals on the bottom so the bottom will be even With the CONJUGATE 4.5 - Complex Numbers

  20. Example 7 Rationalize What is the problem with the bottom? We try to get rid of the radicals on the bottom so the bottom will be even With the CONJUGATE 4.5 - Complex Numbers

  21. Example 8 Rationalize 4.5 - Complex Numbers

  22. Example 9 Rationalize 4.5 - Complex Numbers

  23. Your Turn Rationalize 4.5 - Complex Numbers

  24. Assignment Page 300 23-31 odd, 55-67 odd 4.5 - Complex Numbers

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