Question
Perform the indicated operation \& simplify. Express the answer in terms of \( i \) (as a complex number). \( -4 i(2-6 i)= \)
Ask by Reese Ryan. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( -24 - 8i \)
Solution
Calculate or simplify the expression \( -4i(2-6i) \).
Simplify the expression by following steps:
- step0: Solution:
\(-4i\left(2-6i\right)\)
- step1: Apply the distributive property:
\(-4i\times 2-4i\left(-6i\right)\)
- step2: Multiply the numbers:
\(-8i-4i\left(-6i\right)\)
- step3: Multiply the numbers:
\(-8i-24\)
- step4: Reorder the terms:
\(-24-8i\)
The result of the operation \( -4i(2-6i) \) is \( -24-8i \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To perform the operation, we distribute \(-4i\) into the expression \((2 - 6i)\): \[ -4i(2) + -4i(-6i) = -8i + 24i^2 \] Since \(i^2 = -1\), we can replace \(24i^2\) with \(24(-1)\): \[ -8i - 24 \] Rearranging gives: \[ -24 - 8i \] So, the final answer in terms of \(i\) is: \[ -24 - 8i \]
