Find the product of ( 12 + 6 i ) and its conjugate.

Question

product =   

Answer 1

Use FOIL (First, Outside, Inside, Last products)

(12 + 6i)(12- 6i)

=12(12) -6i(12) + 6i(12) +6i(-6i)

= 144 + (-6+6)i - 36(i^2)

= 144 + 36

= 180

the product of the sum and difference of two numbers

= the difference of the squares of the two numbers

general formula is

(a-b)(a+b) = a^2 - b^2

if a=12 and b= 6i, then

(12-6i)(12+6i) = 12^2 - (6i)^2

= 144-36(-1)

=144+36

= 180