Question

simplify.
(2 + 3i)(-2)
write your answer in the form a + bi.

Explanation:

Step1: Apply distributive property

We use the distributive property (also known as the distributive law of multiplication) which states that for any complex numbers \( (a + bi)(c) = a\times c+bi\times c \). Here, \( a = 2 \), \( b = 3 \), and \( c=- 2 \). So we have:
\((2 + 3i)(-2)=2\times(-2)+3i\times(-2)\)

Step2: Calculate each term

Calculate \( 2\times(-2)=-4 \) and \( 3i\times(-2)=-6i \). Then combine these two results:
\(2\times(-2)+3i\times(-2)=-4-6i\)

Answer:

\(-4 - 6i\)