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

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

Answer: (B)

Verified step by step guidance

1. Distribute the 5 across the terms in the first complex number: \(5(4 + 7i)\). This results in \(5 \times 4 + 5 \times 7i\).
2. Distribute the 6 across the terms in the second complex number: \(6(3 - 2i)\). This results in \(6 \times 3 - 6 \times 2i\).
3. Add the real parts from the results of the distributions: \(20 + 18\).
4. Add the imaginary parts from the results of the distributions: \(35i - 12i\).
5. Combine the sums of the real and imaginary parts to express the final result in standard form: \(38 + 23i\).