Question

simplify. (-10 - i)(-10 + i) write your answer in the form a + bi.

Explanation:

Step1: Apply difference - of - squares formula

We know that $(a - b)(a + b)=a^{2}-b^{2}$. Here, $a=-10$ and $b = i$. So, $(-10 - i)(-10 + i)=(-10)^{2}-i^{2}$.

Step2: Calculate the squares

$(-10)^{2}=100$ and since $i^{2}=-1$, then $(-10)^{2}-i^{2}=100-(-1)$.

Step3: Simplify the expression

$100-(-1)=100 + 1=101+0i$.

Answer:

$101+0i$