5 4 and Numbers Roots 5 4 Complex

5 -4 and Numbers Roots 5 -4 Complex Operations. Numbers with Complex SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Perform operations with complex numbers. Holt Algebra 2 Algebra Holt Mc. Dougal 2

5 -4 Complex Numbers and Roots The imaginary unit i can be raised to higher powers. Helpful Hint Notice the repeating pattern in each row of the table. The pattern allows you to express any power of i as one of four possible values: i, – 1, –i, or 1. SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots Evaluating Powers of i Simplify – 6 i 14 = – 6(i 2)7 = – 6(– 1) = 6 SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots Evaluating Powers of i Simplify i 63. Simplify i 42. SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

Conjugates: What is a conjugate? Factor x 2 – 100. Helpful Hint The complex conjugate of a complex number a + bi is a – bi. Find the conjugate of the following: 1. (4 + i) 2. (i – 3) 3. (4 i)

5 -4 Complex Numbers and Roots Simplify. Dividing Complex Numbers SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots Simplify. SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots The table shows several complex numbers, where i is the imaginary unit. Find the product of each set and put real, imaginary, or complex in the box depending on your answer. 8 – 2 i 3 + 2 i 5 i -4 conjugate SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots Exit Card Perform the indicated operation. Write the result in the form a + bi. 1. (2 + 4 i) + (– 6 – 4 i) 2. (5 – i) – (8 – 2 i) 3. (2 + 5 i)(3 – 2 i) 4. 5. Simplify i 31. SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2

5 -4 Complex Numbers and Roots Homework Finish Worksheet Study for quiz tomorrow! SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. Holt Mc. Dougal Algebra 2