1.3(M2) Warm Up (8 + 4i) – (9 – 2i) (-2 – i) + (-6 – 3i)

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Presentation transcript:

1.3(M2) Warm Up (8 + 4i) – (9 – 2i) (-2 – i) + (-6 – 3i)

Daily Assessment 6 – (-3 + 8i) + 5i (8 + 11i) + (25 + 28i)

1.3 Multiply and Divide Complex Numbers

Vocabulary To multiply two complex numbers, use the distributive property or the FOIL method just as you do when multiplying algebraic expressions. Remember that i=√-1 so . . . i²=-1 Two complex numbers of the form a + bi and a – bi are called complex conjugates. The product of complex conjugates is always a real number.

Examples 1. 6i(-3–7i) 2. (2+4i)(2-6i)

Try these . . . 6i(2 – 4i) (6 – 3i)(2 + 5i) (3 – 8i)²

To Divide Complex Numbers: Rationalize the denominator by multiplying by the conjugate. Examples: 1. 2.

EXAMPLE 5 Divide complex numbers Write the quotient in standard form. 7 + 5i 1  4i

Write the expression as a complex number in standard form. 5 1 + i d. i(9 – i) e. (3 + i)(5 – i) g. 5 + 2i f. 3 – 2i

Try these . . .