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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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5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

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