Question
Perform the indicated operation \& simplify. Express the answer in terms of \( i \) (as a complex number). \( -5 i(9-3 i)=\square \)
Ask by Mann Olson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( -15 - 45i \)
Solution
To simplify the expression \( -5i(9 - 3i) \), follow these steps:
1. **Distribute \( -5i \) across the terms inside the parentheses:**
\[
-5i \times 9 + (-5i) \times (-3i)
\]
This simplifies to:
\[
-45i + 15i^2
\]
2. **Recall that \( i^2 = -1 \):**
\[
-45i + 15(-1) = -45i - 15
\]
3. **Combine the terms to express the result in standard form \( a + bi \):**
\[
-15 - 45i
\]
**Final Answer:**
\( -15 - 45i \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To perform the indicated operation, let's first distribute \(-5i\) into the expression \((9 - 3i)\): \[ -5i(9) + (-5i)(-3i) = -45i + 15i^2 \] Now, since \(i^2 = -1\), we can substitute for \(i^2\): \[ 15i^2 = 15(-1) = -15 \] Now, replace \(15i^2\) in the equation: \[ -45i - 15 \] To express it in standard form, we rewrite it as: \[ -15 - 45i \] So, the final simplified answer is: \[ -15 - 45i = \square \]
