Question

find the product.
(-7 + 5i)(-7 - 5i)

(-7 + 5i)(-7 - 5i)=
(simplify your answer. type your answer in the form a + bi.)

Explanation:

Step1: Apply the difference - of - squares formula

The formula is $(a + b)(a - b)=a^{2}-b^{2}$. Here, $a=-7$ and $b = 5i$. So, $(-7 + 5i)(-7 - 5i)=(-7)^{2}-(5i)^{2}$.

Step2: Calculate the squares

$(-7)^{2}=49$ and $(5i)^{2}=5^{2}\times i^{2}$. Since $i^{2}=-1$, then $(5i)^{2}=25\times(-1)=-25$.

Step3: Subtract the results

$(-7)^{2}-(5i)^{2}=49-(-25)=49 + 25$.

Answer:

$74+0i$