Question

simplify.
(-1 + i)(-3)
write your answer in the form a + bi.

Explanation:

Step1: Distribute -3 to (-1 + i)

Using the distributive property (also known as the distributive law of multiplication over addition), we multiply -3 with each term inside the parentheses. The distributive property states that \( c(a + b)=ca+cb \). Here, \( c = -3 \), \( a=-1 \), and \( b = i \). So we have:
\( (-1 + i)(-3)=(-1)\times(-3)+i\times(-3) \)

Step2: Calculate each product

First, calculate \( (-1)\times(-3) \). The product of two negative numbers is positive, so \( (-1)\times(-3) = 3 \).
Next, calculate \( i\times(-3) \), which is \( -3i \).

Step3: Combine the results

Combining the two results from Step 2, we get \( 3-3i \). In the form \( a + bi \), \( a = 3 \) and \( b=-3 \).

Answer:

\( 3 - 3i \)