Question

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?

Answer 1

foil or distribute

(a+bi)(a-bi)
seems to be a difference of 2 perfect square factored
remember
a^2+b^2=(a+b)(a-b)

so
(a+bi)(a-bi)=(a)^2-(bi)^2
remember, i^2=-1
a^2-(-1b^2)
a^2+b^2

Answer 2

`a^2+b^2`

Explanation:

We are given that (a+ib)(a-ib)

We are given that a and b are both not equal to zero

We have to find the product of (a+ib)(a-ib)

`a(a-ib)+ib(a-ib)`

`a^2-iab+iba-i^2b^2`

We know that
`i^2=-1`

Substitute the value then we get

`a^2-(-1)b^2`

`a^2+b^2`

Hence,
`(a+ib)(a-ib)=a^2+b^2`