https://file.aiquickdraw.com/mathbot/file/1728999251442dkvbd5ho.jpg

The problem asks to multiply:

\[
-3i(2 + 4i)
\]

We will distribute \( -3i \) to each term inside the parentheses.

1. First, multiply \( -3i \) by 2:

\[
-3i \times 2 = -6i
\]

2. Next, multiply \( -3i \) by \( 4i \):

\[
-3i \times 4i = -12i^2
\]

Since \( i^2 = -1 \), this simplifies to:

\[
-12i^2 = -12(-1) = 12
\]

Now, combine the real and imaginary parts:

\[
12 - 6i
\]

Thus, the answer in standard form is:

\[
12 - 6i
\]

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. Multiply \( 5i(3 + 2i) \).
2. Simplify \( (2 + 3i)(1 - 4i) \).
3. Find the product of \( -i(4 + 7i) \).
4. Expand \( (2 - 3i)^2 \).
5. Divide \( \frac{4 + 2i}{1 - i} \) and simplify.

**Tip:** Remember that \( i^2 = -1 \) is key to simplifying complex number products!

Multiply: -3i(2 + 4i). Write your answer as a complex number in standard form.

Learn how to multiply complex numbers with this example of -3i(2 + 4i). The solution involves applying the distributive property and using i^2 = -1 to simplify the expression to 12 - 6i. Suitable for students in Grades 9-12.

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