This lesson covers how to multiply complex numbers using the double distributive property. It begins with a review of the property using algebraic expressions, followed by an explanation of the imaginary unit and common misconceptions. The lesson includes examples of multiplying complex numbers and expanding complex expressions. It also introduces complex conjugates and demonstrates their multiplication. The lesson concludes with a summary of the key concepts.

What is the result of applying the double distributive property to (x + 9)(3x - 2)?

• 3x^2 + 25x - 18

• 3x^2 + 27x - 18

• 3x^2 + 25x + 18

• 3x^2 + 27x + 18

What is the value of i squared?

• 0

• i

• -1

• 1

What is the product of (3 + 2i) and (1 - 5i)?

• -13 + 13i

• 13 + 13i

• 13 - 13i

• -13 - 13i

When expanding (5 - 7i)^2, what is the real part of the result?

• -24

• 49

• 24

• -49

What is the conjugate of the complex number 3 + 9i?

• -3 + 9i

• 3 - 9i

• 3 + 9i

• -3 - 9i

What is the result of multiplying a complex number by its conjugate?

• A real number

• A complex number

• An imaginary number

• Zero

What is the final result of multiplying (-2 + 8i) by its conjugate?

• 16i

• 68

• -68

• 0