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7-9: MORE About Complex Numbers Goal: Be able to solve equations with complex numbers, multiply complex numbers, find conjugates of complex numbers, and divide and find reciprocals of complex numbers. Equality for Complex Numbers If a + bi = c + di then a = c and b = d Ex 1: Solve for x and y. a.) b.)

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Ex 2: Multiply. a.) b.) c.) d.) Remember: i 2 = -1

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e.) f.)

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Complex Conjugates Conjugates: a + bi ; a - bi a.) Ex 3: Find the conjugate of each number. b.) c.) (since 0 + 8i, 0 – 8i are conjugates) d.) (since 4 + 0i, 4 – 0i are conjugates)

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Consider Ex 4: Multiply. a.)

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b.) c.)

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Division and Reciprocals Ex 5: Divide. a.) Multiply by 1; use the conjugate

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Division and Reciprocals Ex 5: Divide. b.) Multiply by 1; use the conjugate

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Ex 6: a.) Find the reciprocal of Multiply by 1; use the conjugate

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Ex 6: b.) Find the reciprocal of Multiply by 1; use the conjugate

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Lesson 1.8 Complex Numbers Objective: To simplify equations that do not have real number solutions.

Lesson 1.8 Complex Numbers Objective: To simplify equations that do not have real number solutions.

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