Question

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

Answer 1

Answer:

$a^2+b^2$

Step-by-step 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, $(a+ib)(a-ib)=a^2+b^2$

Answer 2

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