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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:

\(a^2+b^2\)

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, \((a+ib)(a-ib)=a^2+b^2\)