Respuesta :

apologiabiology
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
lublana

Answer:

[tex]a^2+b^2[/tex]

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)

[tex]a(a-ib)+ib(a-ib)[/tex]

[tex]a^2-iab+iba-i^2b^2[/tex]

We know that [tex]i^2=-1[/tex]

Substitute the value then we get

[tex]a^2-(-1)b^2[/tex]

[tex]a^2+b^2[/tex]

Hence, [tex](a+ib)(a-ib)=a^2+b^2[/tex]