Question

multiply.
(4 + 3i)(4 - 3i)

(4 + 3i)(4 - 3i) =
(type your answer in the form a + bi.)

Explanation:

Step1: Use the difference - of - squares formula

$(a + b)(a - b)=a^{2}-b^{2}$. Here $a = 4$ and $b = 3i$.
$(4 + 3i)(4 - 3i)=4^{2}-(3i)^{2}$

Step2: Calculate the squares

$4^{2}=16$ and $(3i)^{2}=3^{2}\times i^{2}$. Since $i^{2}=-1$, then $(3i)^{2}=9\times(-1)=-9$.
$4^{2}-(3i)^{2}=16-(-9)$

Step3: Simplify the expression

$16-(-9)=16 + 9=25+0i$

Answer:

$25+0i$