Perform the operation and write the result in standard form. -8i(9+3i)

To perform the operation \(-8i(9 + 3i)\), we will use the distributive property to multiply the terms.

\[
-8i(9 + 3i) = -8i \cdot 9 + (-8i \cdot 3i)
\]

Now, let's compute each term:

1. \(-8i \cdot 9 = -72i\)
2. \(-8i \cdot 3i = -24i^2\)

Since \(i^2 = -1\), we substitute \(-1\) for \(i^2\):

\[
-24i^2 = -24(-1) = 24
\]

Now, combine both terms:

\[
-72i + 24
\]

The result in standard form is:

\[
24 - 72i
\]

Would you like a more detailed breakdown, or do you have any questions?

Here are 5 related questions:
1. What is the result of multiplying \(5i(7 - 2i)\)?
2. Can you expand \( (3 + 4i)(1 - 5i) \) and write the result in standard form?
3. What is \(i^3\) and \(i^4\) in terms of \(i\)?
4. How do you find the magnitude of a complex number like \(24 - 72i\)?
5. How can complex numbers be represented on the complex plane?

**Tip:** When multiplying complex numbers, always remember that \(i^2 = -1\), which simplifies the imaginary unit calculations!

Learn how to multiply complex numbers using the distributive property by solving -8i(9 + 3i). This problem demonstrates key concepts of complex numbers and simplifies the result to standard form (a + bi). Suitable for students in Grades 10-12.

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