Question

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 (i) in (4(1 + 3i))
• he added the two complex numbers instead of subtracted

Explanation:

Analyze the original expression and Donte's first step

$$ 4(1 + 3i) - (8 - 5i) $$

Donte's first step:

$$ 4 + 3i - 8 + 5i $$

Identify the error in the distribution

$$ 4(1 + 3i) = 4(1) + 4(3i) = 4 + 12i $$

Donte wrote \(4 + 3i\), which means he did not multiply the \(3i\) term by \(4\).

Match the error to the given options

The error is that he did not apply the distributive property correctly for \(4(1 + 3i)\).

Answer:

• He did not apply the distributive property correctly for 4(1 + 3i) (Correct answer)
• He did not distribute the subtraction sign correctly for 8 - 5i
• He added the real number and coefficient of i in 4(1 + 3i)
• He added the two complex numbers instead of subtracted