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 across the terms inside each parenthesis: multiply 5 by both 4 and 7i, and multiply 6 by both 3 and -2i. This gives \$5 \times 4 + 5 \times 7i\( and \)6 \times 3 + 6 \times (-2i)$.
3. Write out the distributed terms explicitly: \$20 + 35i + 18 - 12i$.
4. Combine like terms by adding the real parts together and the imaginary parts together: \((20 + 18) + (35i - 12i)\).
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.