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4.6 Perform Operations With Complex Numbers

Learn about complex numbers, the imaginary unit "i", and how to perform operations such as addition, subtraction, multiplication, and division. Practice problems provided.

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4.6 Perform Operations With Complex Numbers

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  1. 4.6 Perform Operations With Complex Numbers

  2. Vocabulary: • Imaginary unit “i”: defined as i = √-1 • : i2 = -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.

  3. Example: • (ex) 2x2 + 11 = -37

  4. Practice Problems: • Page 275 (1-6)

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

  6. Adding and Subtracting Complex Numbers • (ex) (8 – i) + (5 + 4i) • Combine like terms: • (8 + 5) + (- i + 4i) • 13 + 3i

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

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

  9. 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.

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