Question

find the following product and write the result in standard form, a + bi. (-1 + i)(-1 - i) (-1 + i)(-1 - i) = \square

Explanation:

Step1: Use difference of squares

Recall $(a+b)(a-b)=a^2-b^2$, here $a=-1$, $b=i$

$$\begin{align*} (-1+i)(-1-i)&=(-1)^2 - (i)^2 \end{align*}$$

Step2: Compute each squared term

Calculate $(-1)^2$ and $i^2=-1$

$$\begin{align*} (-1)^2 - (i)^2&=1 - (-1) \end{align*}$$

Step3: Simplify the expression

Perform the subtraction of negative value

$$\begin{align*} 1 - (-1)&=1+1=2 \end{align*}$$

Answer:

$2$ or $2+0i$