QuestionAugust 26, 2025

Simplify. 4i(-6+8i) Enter your answer in the box in standard form. square

Simplify. 4i(-6+8i) Enter your answer in the box in standard form. square
Simplify. 4i(-6+8i) Enter your answer in the box in standard form. square

Solution
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Answer

-32 - 24i Explanation 1. Distribute the term Multiply 4i with each term inside the parentheses: 4i \cdot (-6) + 4i \cdot (8i). 2. Simplify each multiplication 4i \cdot (-6) = -24i and 4i \cdot (8i) = 32i^2. 3. Use the property of i^2 Since i^2 = -1, replace 32i^2 with 32(-1) = -32. 4. Combine real and imaginary parts Combine -32 (real part) and -24i (imaginary part) to get -32 - 24i.

Explanation

1. Distribute the term<br /> Multiply $4i$ with each term inside the parentheses: $4i \cdot (-6) + 4i \cdot (8i)$.<br /><br />2. Simplify each multiplication<br /> $4i \cdot (-6) = -24i$ and $4i \cdot (8i) = 32i^2$.<br /><br />3. Use the property of $i^2$<br /> Since $i^2 = -1$, replace $32i^2$ with $32(-1) = -32$.<br /><br />4. Combine real and imaginary parts<br /> Combine $-32$ (real part) and $-24i$ (imaginary part) to get $-32 - 24i$.
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