Certainly! Let's solve the expression step-by-step:
Given the expression:
[tex]\[ -3 \cdot (10i + 6) \][/tex]
we distribute [tex]\(-3\)[/tex] to both terms inside the parentheses:
1. First, distribute [tex]\(-3\)[/tex] to [tex]\(10i\)[/tex]:
[tex]\[ -3 \cdot 10i = -30i \][/tex]
2. Next, distribute [tex]\(-3\)[/tex] to [tex]\(6\)[/tex]:
[tex]\[ -3 \cdot 6 = -18 \][/tex]
Now, combine the results of these operations:
[tex]\[ -18 - 30i \][/tex]
So, the final answer is:
[tex]\[ -3 \cdot (10i + 6) = -18 - 30i \][/tex]
To summarize, when you multiply [tex]\(-3\)[/tex] by the complex number [tex]\(10i + 6\)[/tex], you get [tex]\(-18\)[/tex] (the real part) and [tex]\(-30i\)[/tex] (the imaginary part), resulting in [tex]\(-18 - 30i\)[/tex].
