To analyze the solution step by step, let's begin by understanding the original expression and follow the student's steps:
The initial problem is to multiply [tex]\(2i\)[/tex] by [tex]\((-8i + 3)\)[/tex].
Step 1: Distribute [tex]\(2i\)[/tex] across [tex]\((-8i + 3)\)[/tex]:
[tex]\[ 2i (-8i) + 2i (3) \][/tex]
Step 2: Compute each term.
- For the first term: [tex]\( 2i \times -8i = -16i^2 \)[/tex]
- For the second term: [tex]\( 2i \times 3 = 6i \)[/tex]
Putting them together, we get:
[tex]\[ -16i^2 + 6i \][/tex]
Step 3: Substitute [tex]\(i^2\)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[ -16(-1) + 6i \][/tex]
Step 4: Simplify the expression:
[tex]\[ 16 + 6i \][/tex]
So:
[tex]\[ 16 + 6i \][/tex]
Comparing this solution with the expected outputs:
The correct product in the form of [tex]\(a + bi\)[/tex] is [tex]\( 16 + 6i \)[/tex].
Here are the steps where the student computationally did everything right. The error is not evident because the final expression [tex]\(16 + 6i\)[/tex] matches the expected product.
Thus, no step contains a computational error.
