Find the product of 3-4i and its conjugate.

Remember that i²=-1

the conjugate of a+bi is a-bi

so

3-4i

the conjugate is 3+4i

product

(3-4i) (3+4i)

hey, this looks familiar

remember (a-b) (a+b) = a²-b²

so

(3-4i) (3+4i) = (3) ² - (4i) ²=9 - (16i²) = 9-16 (-1) = 9+16=25

the product is 25

it's conjugate is 3+4i