Find the sum. Express your answer in standard form.
$5(4+7i)+6(3-2i)$

• A. $7+5i$
• B. $38+23i$
• C. $2+47i$
• D. $7+9i$

Answer: (B)

Verified step by step guidance

1. Identify the expression to simplify: \$5\left(4+7i\right) + 6\left(3-2i\right)\(, where \)i$ is the imaginary unit.
2. Distribute the constants to each term inside the parentheses: multiply 5 by both 4 and \$7i\(, and multiply 6 by both 3 and \)-2i\(. This gives \)5 \times 4 + 5 \times 7i + 6 \times 3 + 6 \times (-2i)$.
3. Rewrite the expression after distribution as \$20 + 35i + 18 - 12i$ by performing the multiplications.
4. Combine like terms by adding the real parts together (\$20 + 18\() and the imaginary parts together (\)35i - 12i$).
5. Express the final sum in standard form \(a + bi\), where \(a\) is the sum of the real parts and \(b\) is the sum of the imaginary coefficients.