Donte simplified the expression below. 4(1+3i)-(8-5i) 4+3i-8+5i -4+8i What mistake did Donte make? He did not apply the distributive property correctly for 4(1+3i) He did not distribute the subtraction sign correctly for 8-5i He added the real number and coefficient of in 4(1+3i) He added the two complex numbers instead of subtracted.

To identify the mistake Donte made, let's go through the steps of simplifying the expression \(4(1+3i)-(8-5i)\) correctly.<br /><br />1. **Apply the distributive property to \(4(1+3i)\):**<br /> \[<br /> 4(1+3i) = 4 \cdot 1 + 4 \cdot 3i = 4 + 12i<br /> \]<br /><br />2. **Subtract \(8-5i\) from \(4 + 12i\):**<br /> \[<br /> (4 + 12i) - (8 - 5i)<br /> \]<br /><br />3. **Distribute the subtraction sign:**<br /> \[<br /> 4 + 12i - 8 + 5i<br /> \]<br /><br />4. **Combine like terms (real parts and imaginary parts):**<br /> \[<br /> (4 - 8) + (12i + 5i) = -4 + 17i<br /> \]<br /><br />So, the correct simplification of the expression \(4(1+3i)-(8-5i)\) is \(-4 + 17i\).<br /><br />Now, let's compare this with Donte's steps:<br /><br />1. \(4(1+3i)-(8-5i)\)<br />2. \(4+3i-8+5i\)<br /><br />Donte's mistake occurred in the second step. He did not distribute the subtraction sign correctly. Instead of subtracting \(8-5i\), he added the terms incorrectly.<br /><br />Therefore, the correct answer is:<br />**He did not distribute the subtraction sign correctly for \(8-5i\).**