4.6 Perform Operations With Complex Numbers. Vocabulary: Imaginary unit “i”: defined as i = √-1 : i 2 = -1 Imaginary unit is used to solve problems that.

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4.6 Perform Operations With Complex Numbers

Vocabulary: Imaginary unit “i”: defined as i = √-1 : i 2 = -1 Imaginary unit is used to solve problems that create a negative inside the square root. You can not take the square root of a negative number with using the imaginary unit.

Example: (ex) 2x = -37

Practice Problems: Page 275 (1-6)

Complex Numbers Complex Number: (Standard Form): a + bi a = real part b = imaginary part a + bi is an imaginary number.

Adding and Subtracting Complex Numbers (ex) (8 – i) + (5 + 4i) Combine like terms: (8 + 5) + (- i + 4i) i

(Ex) (7 – 6i) - (3 – 6i) (ex) 10 – (6 + 7i) + 4i

Multiply Complex Numbers (ex) 4i(-6 + i) Distribute (ex) (9 – 2i) (-4 + 7i) Foil Method

Divide Complex Numbers Complex Conjugates: a + bi is a conjugate of a – bi. (ex) 7 + 5i 1 + 4i Multiply the numerator and denominator by the conjugate.