Multiplying Complex Numbers (1.12.4)

Question 1

• i = sqrt-1. This is called an imaginary number because there are no examples of a number which multiplies with itself to produce a negative number. Therefore, no one knows what the square root of a negative might be; it must be imaginary.

Answer 1

• i = sqrt-1. This is called an imaginary number because there are no examples of a number which multiplies with itself to produce a negative number. Therefore, no one knows what the square root of a negative might be; it must be imaginary.

Question 2

• i^2 = -1. This follows from the definition of a square root. If you multiply a square root times itself, you get the base being rooted.

Answer 2

• i^2 = -1. This follows from the definition of a square root. If you multiply a square root times itself, you get the base being rooted.

Question 3

• FOIL: Multiply binomials by multiplying
First terms together
Outer terms together
Inside terms
Last terms, and adding all the products together

Answer 3

• FOIL: Multiply binomials by multiplying
First terms together
Outer terms together
Inside terms
Last terms, and adding all the products together