Lesson 7-9 More Complex Numbers Objectives Students will: Solve equations with complex numbers Multiply complex numbers Find conjugates of complex numbers.

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Presentation transcript:

Lesson 7-9 More Complex Numbers Objectives Students will: Solve equations with complex numbers Multiply complex numbers Find conjugates of complex numbers Simplify quotients involving complex numbers

Solving Equations If a + bi = c + di, then the real parts must equal as well as the imaginary parts: a = c and b = d 1)set the real parts equal to each other 2)set the imaginary parts equal 3)solve each Example 1 5x + 6i = yiExample 2 4x + 2yi = 8 + 6i

Multiplying Treat i as a variable when distributing (foiling) Change any i 2, i 3,… after Example 3 (2 + 5i)(3 + 4i) Conjugates The conjugate of a + bi is a – bi The product of complex conjugates is the real #: a 2 + b 2 Example 4 Example 5 (4 + 2i)(4 – 2i) Conjugate of -2 – 5i

Dividing & Reciprocals We need to get rid of complex numbers in the denominator Method: use the conjugate as a fraction equivalent to 1 Example 6Example 7 HW 88