Find the product and write the result in standard form. −8i(8i−6)

To find the product of \( -8i(8i - 6) \), we will apply the distributive property.

\[
-8i(8i - 6) = (-8i \cdot 8i) + (-8i \cdot -6)
\]

Now, compute each term:

1. \( -8i \cdot 8i = -64i^2 \)
2. \( -8i \cdot -6 = 48i \)

Next, simplify \( -64i^2 \). Recall that \( i^2 = -1 \), so:

\[
-64i^2 = -64(-1) = 64
\]

Now, the expression becomes:

\[
64 + 48i
\]

Thus, the result in standard form is:

\[
64 + 48i
\]

Would you like any further clarification or details?

Here are 5 related questions to practice:

1. Simplify \( 5i(7i + 4) \) and write the result in standard form.
2. Multiply and simplify: \( (3i)(4i - 9) \).
3. What is the product of \( 2i(6 - 10i) \)?
4. Find the result of \( -5i(8i + 7) \) in standard form.
5. Expand and simplify \( (2 + 3i)(4 - i) \).

**Tip:** Always remember that \( i^2 = -1 \) when simplifying powers of \( i \).

Learn how to multiply and simplify complex numbers with the expression −8i(8i−6). This problem demonstrates the distributive property and how to simplify using the imaginary unit i^2 = -1. Suitable for students in Grades 9-12.

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