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. Distribute the constants outside the parentheses to each term inside the parentheses. For the first part, multiply 5 by both 4 and 7i, and for the second part, multiply 6 by both 3 and -2i. This gives you: \$5 \times 4 + 5 \times 7i\( and \)6 \times 3 + 6 \times (-2i)$.
2. Write the expression after distribution as: \$20 + 35i + 18 - 12i$.
3. Group the real parts together and the imaginary parts together. That means combine \$20\( and \)18\( for the real part, and combine \)35i\( and \)-12i$ for the imaginary part.
4. Add the real numbers: \$20 + 18\(, and add the imaginary numbers: \)35i - 12i$ separately.
5. Write the final expression in standard form as \(a + bi\), where \(a\) is the sum of the real parts and \(b\) is the sum of the imaginary parts.